TL/DR: I stayed in a hotel and haven't been billed yet. At what point am I no longer legally responsible for the debt?
I used a well known website (expedia) to book a hotel room for a week in a small bed and breakfast in a small seasonal town in the US (Massachusetts). I made the booking approximately 6 months prior to my stay during the middle of the off season. The terms were that my credit card on file would be billed directly by the hotel for a 1 night deposit immediately and the rest after I completed my stay. I was immediately billed my deposit as expected, but I was also billed the remaining balance in a second charge. I was also issued a credit within 24 hours for the remaining balance. Someone caught this before I did and it all magically appeared on my statement.
4 months later, at the beginning of the busy season, I received a welcome email explaining how the B&B works and where I would find the keys and how to check-in and check-out. That day my credit card was again billed the remaining balance and a credit was again issued within 24 hours. During my stay I never saw anyone from the B&B. The keys were where they were supposed to be and I left them where I was instructed. Upon checking out, my credit card was again billed the remaining balance, as I would expect. Unexpectedly, within 24 hours, I was issued another credit.
I have never been contacted by my credit card company fraud department. I believe the hotel is just inept. If they manage to bill my credit card correctly, I will pay the bill and not dispute the charge as it is what I agreed to. That said, while normally I would be upfront with the hotel and try and pay my bill proactively, in this case I don't want to since I wasn't particularly happy with the hotel. Further, they seem to be so inept that I worry that saying something will cause them to bill me multiple times again.
At what point am I no longer legally responsible for the charges? Can they go through their books in 10 years and realize I never paid and charge me?
EDIT In response to a now-deleted suggestion that it's unreasonable not to be more proactive, the hotel was not a traditional B&B, but it only had 6 rooms and was a small family run operation. My unmet expectations were related to the quality of the amenities. There was supposed to be a private beach for the hotel, but the beach was only accessible during the lowest of low tides and even then you had to sit under the pylons holding up the hotel. More problematic was the hotel advertised that the room came with two kayaks, which it did, but it didn't come with paddles or life jackets. Similarly, the room was advertised to have bikes, but they had flat tires. We eventually got in touch with the staff via email and they responded that they knew about the problems, but couldn't fix them during our stay. None of these issues was enough for me to withhold payment or ask for a refund, but it does make me less inclined to point out their errors.