There are a few places you can "idle" your character legitly. Depends on where you are though.
1) Try to run out the first door from outer cloister towards the pit, if you run at an angle you will get "stuck" behind the door, perpetually running. As this is not in town, you have to make sure the surroundings are clear of any mosters.
2) In Harrogath you can get this "running effect either by:
a) Stand on the little platform up the stairs from your stash. Click on the stash. If you stand at the right spot (near one of the torches) you will not actually go to the stash but stay where you are.
b) Go out of town and make a tp. go into Malah's house and click on the tp. same effect.
3) There is apparently some similar trick in the rouge encampment, but i never used it, so i dont know how it works.
Of course you can still get connection interrupted and get kicked out of the game, but at least you wont time out.