I got Linksys WRT54GL with Tomato custom firmware v1.28.1812 (Built on Mon, 03 May 2010 20:35:16 -0700). LT2P reconnect at 012 doesn't happen too often, but sometimes changes unexpectedly.
How you feel that? Browsers can not open sites, any other program you start after reconnection that require internet communication also will fail reporting that their servers are not accessible. But already connected applications like messengers (Skype, GTalk, etc) that were connected before redial still working because they usually no need extra DSN lookups once they online.
This is an example of log after reconnect.
May 19 20:05:22 linksys daemon.notice pppd[10267]: Modem hangup
May 19 20:05:22 linksys daemon.notice pppd[10267]: Connection terminated.
May 19 20:05:22 linksys daemon.info pppd[10267]: Connect time 2761.3 minutes.
May 19 20:05:22 linksys daemon.info pppd[10267]: Sent 2694942685 bytes, received 2221543095 bytes.
May 19 20:05:23 linksys daemon.info pppd[10267]: Exit.
May 19 20:05:44 linksys user.info redial[10265]: WAN down. Reconnecting...
May 19 20:05:47 linksys user.info kernel: vlan1: del 01:00:5e:11:11:22 mcast address from master interface
May 19 20:05:47 linksys user.info kernel: vlan1: del 01:00:5e:11:11:22 mcast address from vlan interface
May 19 20:05:47 linksys user.info kernel: vlan1: del 01:00:5e:14:41:22 mcast address from master interface
May 19 20:05:47 linksys user.info kernel: vlan1: del 01:00:5e:14:41:22 mcast address from vlan interface
May 19 20:05:47 linksys user.warn kernel: vlan1: Setting MAC address to 00 23 69 3b 47 29.
May 19 20:05:47 linksys user.info kernel: vlan1: add 01:00:5e:14:41:22 mcast address to master interface
May 19 20:05:47 linksys user.info kernel: vlan1: add 01:00:5e:11:11:22 mcast address to master interface
May 19 20:05:48 linksys user.info kernel: IPP2P v0.8.1_rc1 unloaded
May 19 20:05:50 linksys user.info redial[21003]: Started. Time: 30
May 19 20:05:51 linksys daemon.notice pppd[21005]: pppd 2.4.1 started by root, uid 0
May 19 20:05:51 linksys daemon.info pppd[21005]: Using interface ppp0
May 19 20:05:51 linksys daemon.notice pppd[21005]: Connect: ppp0 <--> /dev/pts/0
May 19 20:05:51 linksys daemon.notice pppd[21006]: pppd 2.4.1 started by root, uid 0
May 19 20:05:51 linksys daemon.info pppd[21006]: Using interface ppp1
May 19 20:05:51 linksys daemon.notice pppd[21006]: Connect: ppp1 <--> /dev/pts/1
May 19 20:05:53 linksys daemon.err pppd[21005]: not replacing existing default route to vlan1 [172.27.48.1]
May 19 20:05:53 linksys daemon.notice pppd[21005]: local IP address 80.178.17.224
May 19 20:05:53 linksys daemon.notice pppd[21005]: remote IP address 212.199.17.75
May 19 20:05:53 linksys daemon.notice pppd[21005]: primary DNS address 80.179.52.100
May 19 20:05:53 linksys daemon.notice pppd[21005]: secondary DNS address 212.116.161.40
May 19 20:05:53 linksys daemon.info dnsmasq[10272]: exiting on receipt of SIGTERM
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: started, version 2.52 cachesize 150
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: compile time options: no-IPv6 GNU-getopt no-RTC no-DBus no-I18N DHCP no-scripts no-TFTP
May 19 20:05:53 linksys daemon.info dnsmasq-dhcp[21012]: DHCP, IP range 12.13.14.31 -- 12.13.14.39, lease time 1d
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: reading /etc/resolv.dnsmasq
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: using nameserver 212.116.161.40#53
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: using nameserver 80.179.52.100#53
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: read /etc/hosts - 0 addresses
May 19 20:05:53 linksys daemon.info dnsmasq[21012]: read /etc/hosts.dnsmasq - 73 addresses
May 19 20:05:54 linksys user.info kernel: IPP2P v0.8.1_rc1 loading
May 19 20:05:56 linksys daemon.err pppd[21006]: not replacing existing default route to ppp0 [212.199.17.75]
May 19 20:05:56 linksys daemon.notice pppd[21006]: local IP address 80.178.21.137
May 19 20:05:56 linksys daemon.notice pppd[21006]: remote IP address 212.199.17.74
May 19 20:05:56 linksys daemon.notice pppd[21006]: primary DNS address 80.179.52.100
May 19 20:05:56 linksys daemon.notice pppd[21006]: secondary DNS address 80.179.55.100
May 19 20:05:56 linksys daemon.info dnsmasq[21012]: reading /etc/resolv.dnsmasq
May 19 20:05:56 linksys daemon.info dnsmasq[21012]: using nameserver 80.179.55.100#53
May 19 20:05:56 linksys daemon.info dnsmasq[21012]: using nameserver 80.179.52.100#53
May 19 20:05:56 linksys daemon.info dnsmasq[21012]: exiting on receipt of SIGTERM
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: started, version 2.52 cachesize 150
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: compile time options: no-IPv6 GNU-getopt no-RTC no-DBus no-I18N DHCP no-scripts no-TFTP
May 19 20:05:56 linksys daemon.info dnsmasq-dhcp[21059]: DHCP, IP range 12.13.14.31 -- 12.13.14.39, lease time 1d
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: reading /etc/resolv.dnsmasq
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: using nameserver 80.179.55.100#53
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: using nameserver 80.179.52.100#53
May 19 20:05:56 linksys user.info kernel: vlan1: del 01:00:5e:11:11:22 mcast address from master interface
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: read /etc/hosts - 0 addresses
May 19 20:05:56 linksys daemon.info dnsmasq[21059]: read /etc/hosts.dnsmasq - 73 addresses
May 19 20:05:58 linksys user.info kernel: vlan1: add 01:00:5e:11:11:22 mcast address to master interface
May 19 20:06:21 linksys user.info kernel: vlan1: del 01:00:5e:11:11:22 mcast address from master interface
May 19 20:06:23 linksys user.info kernel: vlan1: add 01:00:5e:11:11:22 mcast address to master interface
May 19 21:05:14 linksys daemon.info dnsmasq[21059]: reading /etc/resolv.dnsmasq
May 19 21:05:14 linksys daemon.info dnsmasq[21059]: using nameserver 192.168.101.102#53
May 19 21:05:14 linksys daemon.info dnsmasq[21059]: using nameserver 192.168.101.101#53
May 19 21:05:14 linksys daemon.info dnsmasq[21059]: exiting on receipt of SIGTERM
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: started, version 2.52 cachesize 150
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: compile time options: no-IPv6 GNU-getopt no-RTC no-DBus no-I18N DHCP no-scripts no-TFTP
May 19 21:05:14 linksys daemon.info dnsmasq-dhcp[21564]: DHCP, IP range 12.13.14.31 -- 12.13.14.39, lease time 1d
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: reading /etc/resolv.dnsmasq
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: using nameserver 192.168.101.102#53
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: using nameserver 192.168.101.101#53
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: read /etc/hosts - 0 addresses
May 19 21:05:14 linksys daemon.info dnsmasq[21564]: read /etc/hosts.dnsmasq - 73 addresses
Note the last 4 lines about nameserver, it takes 192.168.101.102#53 and 192.168.101.101#53.
The workaround is to set static DNS. I saw that 012 usually reports 3 addresses: 80.179.52.100, 80.179.55.100 and 212.116.161.40.
So I set first two from 012 and third from Google public DNS (just in case first two fails): 80.179.52.100, 80.179.55.100 and 8.8.8.8.