Yes, any new instance of a Transaction Object will create a new thread over to ASE.
AFAIK: If you use the one TO, you cannot issue multiple requests to ASE. Your 2nd thread is always stalemated and thus has no effect.
If another application is terminating the connection at the network level - there is not much you can do about it. I would talk to your network & DBA guys and see if there is a way around this situation.