Every situation is different, so there may be reasons to simply bend over for them, but you are enabling and enforcing their behavior and making all the other landlords out there have to work that much harder to compensate.

You let this go, it becomes learned behavior, and she may start paying whenever you want.That's the principle.  

Is this behavior within the rules of the site?"

Personally I would take care of the repair as a show of good faith and understand that this behavior fosters a good relationship between landlord/tenant.  

That's just more of the same outsourcing behavior that has gotten ou into this situation. 

I don't believe in financially rewarding bad behavior.

People who have incidents of domestic violence in their history often repeat the behavior.  

Being part of the solution means doing what you can to discourage unethical behavior - reporting the agent, refusing to deal with him.

A lax PM company, or owner, can encourage all kinds of behavior that isn't optimal for you - did they have preexisting leases?

CORPORATE GOVERNANCE The board of directors of a non-bank mortgage servicer should establish a sound corporate governance framework to protect the financial interests of the firm’s stakeholders and set minimum standards of acceptable behavior for employees in the business.