sometimes there is the best one could do and then there is the best a specific person can do.
I once complained to somene about my abusive stepfather and they explained that like it or not he was doing his best. He stated it may not be what I consider to be the best or be the best but it was /his best/. and he was right its true.
while sometimes we may fall short of some standard best we can be or best somene thinks we can be so long as we are doing the best that we can thats all that matters.
I know in my drunken days I was doing the best that i could. It may not have been all that great since i was under the influence etc.. But i was the best that I had at the time given the circumstances.