Well bypassing a legitimate time limit stupid or otherwise (you don't say what this limit is or why it is set) would I'm sure contravene the sites terms and conditions.
Personally that aside I don't know if using a proxy would get round this time limit anyway, it is obviously cleaver enough to have avoided what you have tried. If you are concerned with hiding your IP then that wouldn't make a blind bit of difference as the IP of the proxy wouldn't have changed in the session that would be timed.
There are many way you can monitor a time limit for a session and I'm sure most of them wouldn't be invalidated just by using a proxy.