There are several banks in Grand Theft Auto 5 that seem ripe for the picking, but are you able to rob them any time you want?
Unfortunately it appears that you can’t, and that you can only rob them via heist missions.
Also, you can’t replay heist missions to gather more money either, since it saves your game before hand. You can only replay heist missions to gain a better rating.
Apparently you may be able to do so in GTA Online however, and likely with your online crews.
This is a little disappointing in my opinion. This would definitely add to the replay value of the game if it was possible.
Maybe this was intended to be a GTA Online only feature though, which is where the replay value will likely be.