Presumably you are expecting the Procedure to "take a long time" ?
And you are thinking that the 10-minutes, being a nice round number, is a timeout somewhere. Sounds like it to me too. Dunno how to fix that, but:
Any chance that you could Launch a task (at the Sybase end) to do the (long running) job, and then come back later and view the results - such that neither of those two things would take more than 10 minutes?
PITA but if you are in a hurry to get something working maybe that would do as a stop-gap.
Hopefully someone else knows where the 10-minute-timeout setting is. Short of the Client disconnecting, I think the server-to-server actions I have done with Linked Servers will run forever, until completion, unless I put a time limit on them.