It turns out my phone has a weird bug. Actually, i'm not sure if it's my phone, all Nexus Ones, all phones with this version of Android, all phones with this GPS chip or what. But in any case, every so often my phone apparently gets in a weird state where it can get an initial GPS fix, but can't do constant tracking. So once this bug kicked in all the apps that use GPS would seem to start up okay, but then fail shortly thereafter.
Luckily when the CardioTrainer app lost the GPS connection it suggested i should try rebooting my phone, which fixed it!
So i've finally gotten a real Zombies 5k run in!
In not so good news, after doing 4 runs in two weeks i'm definitely starting to get at least one blister. There's a white oval patch underneath one of the calluses on my right foot =P