Does a company that loses a check have an obligation to pay my stop payment charge?

I paid $50 for the cable company to hook up high speed internet. There is no way to give the money directly to the cable company; I have to leave it with the leasing office at my complex, then they give it to the cable company (both owned by the same person). The cable company claims that they never got the check and the leasing office says they gave it to the cable company. Now I have to pay a $32 stop payment fee to my bank. Are they required to pay that, and can I deduct it from the $50?

Do they have an obligation? No. But they should pay the charge as a matter of principle. Like Barky stated, it's your word against theirs. Good luck getting them to admit they might be wrong.

Well, from their point of view it's your word against theirs. Anyone could say they gave the payment when they really didn't. I'm sure you've checked your bank to make sure it hasn't cleared but if you haven't then do so.
I work for a company who only accepts cash or checks so I deal with this a lot. If it's a regular customer who always pays on time and a check is lost then I'll note the account (with date and check number) and give it about a month to show. If it doesn't then I may split the fee with them. But do I have an obligation to pay the stop payment? NO. And really, to pay $32 for a $50 check seems silly. It's probably in the trash somewhere and no one will ever find it. I'd ask for some time from them for it to show up, if it doesn't then write a new one. If it ever clears your bank take the statement to leasing company and show them.