It would depend on whether or not the landlord is accepting your payments as rent or use and occupancy payments. If it is being accepted without reservation, then it can be construed as rent, therefore entering you into a new term of tenancy. If that is the case, the landlord would have to terminate your rights to tenancy again by way of notice to quit. Obtain a copy of your returned cashed checks from your bank - look to see if they have use and occupancy or anything else written on them. That will go a long way toward determining your current rights.
If you have been paying rent since May 1 then it is likely (but not guaranteed) that the landlord would have to send a new notice to quit.
Do you want accurate, personalized, legal advice that you can rely on? You will have to hire an attorney, not ask on Avvo. I am not your attorney and am not creating an attorney-client relationship by this post. I am therefore giving only general advice. This advice may not apply to you or your situation; may not take account of all possibilities, and may not match the advice I would give to a client. DO NOT rely on this advice or any other advice on Avvo to make your legal decisions. If you want an answer to a legal question you should retain an attorney who is licensed in your state.
It depends on whether or not your landlord reserved their rights to evict you and if they are accepting your payments as use and occupancy or as rent. That said, a court may still find that given the amount of time that has elapsed and the acceptance of payments has reinstated your tenancy. If you have concerns, you may want to bring any rental documents and notices to a landlord/tenant law attorney for review.
This "answer" is for information purposes only and is not intended as legal advice or to create an attorney-client relationship.