I’ve always relied upon the generosity of people to part-lease their horses in the kind of informal, month-to-month situations you’ve described. One thing to consider is that the owner has probably had pretty significant vet bills with an unsound horse. Not only isn’t there anything in writing saying you’re owed a refund if the horse isn’t sound, but unless you’re paying a hefty lease fee, probably the owner won’t be very sympathetic that she’s dealing with a horse she owns who is has been unsound and unrideable, and that she’s responsible for whether he can be ridden or not.
However, if this becomes a significant issue in the future, since it is just a lease, not a horse you own, I’d have a think about whether you want to continue with it, if the horse continues to have issues. Make sure to discuss with the owner well in advance so she can plan financially for the loss of the fee.
The only time I’ve seen compensation for a leased and unsound horse was at barns that leased as part of a “program,” where the horse would be leased to a rider for say, three days a week, for one lesson and two days of hacking. Sometimes the owner/trainer would allow the student use of another horse she owned for the lesson day (without charging a fee), but that was in her financial interest (so she didn’t lose income for the lesson).