Other members can attack you even when you are not logged in to the game. This is to be expected. But, for revenge or another reason, some members will target you because they see you as weaker or richer. This is not usually a problem when the other member is almost even with use strength-wise. It becomes a major problem when the other member, while being at nearly the same level, has more money, weapons or a lot of strong members in their mafia. They can attack you at will, as much as they want. 

I had one such member attack me last week. He robbed my properties dozens and dozens of times. I lost about $60 million preparing and protecting my casinos because he kept attacking and attacking.

What can you do when a member keeps attacking and robbing you? You can wait for them to get bored with you or you can be pro-active. There are two ways that I found to combat the situation. The first is to add the member to the hit list with a sizable bounty and hope that a really stronger member attacks your enemy. However, if this does not work and you keep getting attacked, the last resort is to sell off your properties, especially the big ones, and wait a few days for your enemy to get bored with you and move on. You can always buy your properties again; it is just a minor setback.

When you get stronger and gain more members, you can always go back and enact revenge on the person that repeatedly attacked you. Copy and save the link location to this member for future use. At least, that is what I would do but, I am a very vengeful person!