You have accurately located the law applicable to the legal issue presented.
I would consider the application of the law to this fact pattern to be a close call that reasonable people could interpret either way.
Your suggestion that the right to access lasts until the maintenance request is completed is a pretty attractive bright line to draw between when access is allowed and when it isn't under the circumstances.
In the absence of evidence that the landlord has abandoned the maintenance order, so long as the work isn't done and someone is continuing to do work for the problem described in the order (and as you notnote parenthetically, this is surely what is going on) the landlord is probably in the right here. Also, it isn't terribly out of the ordinary for it to take weeks to get a repair job fixed. At some point, maybe a year or two, the claim that the landlord abandoned the maintenance order might look more plausible, but those aren't your facts.