Agreed with respect to not letting them move in. Understand though that you essentially are starting over with regards to timelines. If the broker has to shop for a new loan you will need to reset the clock with regards to loan contingency and possibly even the appraisal contingency.
Second, I am concerned about the line of B of A not honoring the loan committment. I would ask for more details including documentation why they basically declined the loan. There needs to be some sort of reason behind the decline especially if you are this far in.
Another possible alternative is for you to agree to give them the extension, however you can state that you are concerned with their viability as buyers. That you will need some sort of compensation if they go through another 1-2 week period and get declined yet again. The fact that the are only coming in with 10% down means they are not going conventional as well. So maybe they pony up a little bit more of a deposit or make some of the deposit non refundable.
They probably will not bite on it. Also as slow as things were the past few months I am actually seeing a little bit more activity. However this may be confined to certain regions so I cannot comment on your area. It would depend on how things are where you are at, how long your home was on the market, how much activity you had, etc…