Them - connections always time out
You - connections always stay open
Or you didn't ask and they didn't tell.
The current and future relationship should determine who should pay.
Ask them to absorb all the fines. If they refuse, ask for split. If they refuse, pay the fine and look for another partner.
IANAL, so that may be just too much common sense. Of course this is just IMHO.
You may need to question the IT person who reviewed the SLA and failed to raise the timeout question.