When I last played there was still a bug with Agents/Smugglers going into cover that could cause a player to stop auto-running. This might be the problem.

Generally speaking, with any elevator you had best move onto and off of them manually. Otherwise all sorts of wackiness happens with the auto-following character.

There is also the odd quest area Republic side that I ran into where auto-follow simply doesn't work and the follower(s) will try to run out of the instance.