Yes. They have to give you new one if that one is defective. Call them and bug them non-stop. You are paying all that money for stable service... ok, we can not expect to have perfectly stable service, but still... for that money, it's totally unacceptable to lose your connection every few hours... call their technical support and they must locate the problem. Even from there, they can check what gives you those problems. They have to go by the system of elimination, and finally they'll find solution.
Call them right away, and report those issues. If you already eliminated your software, and you are 100% sure your firewall and antivirus don't give you those problems, then the ball is in their field... they have to make a move now. Bottom line, they all offers those 24/7 technical support... so, why not use it ? Don't be afraid, that's your right as a valued customer.
Cheers !