If you are on a monthly plan, make sure you keep your payments up to date, or else they can revert back to available at Network Solutions, and someone can buy it right out from under you. Naturally, you would lose the whole of the website as well.
That happened to me with one of my sites, only in this case, the hosting company did not propagate the DNS correctly, so the domain name was supposedly up for grabs, and then it was sold by Network Solutions to someone who bought a 5 year hosting package, which apparently is then non-refundable.
My hosting company then suggested I try to get the name back for $100.
But all credit to Network Solutions and a reasonable woman who was not thieving my domain, merely caught in the confusion, and I got it back.
The one other thing to note here is that the hosting company was still happily billing me automatically every month. I eventually got the money applied to my account, but it was pretty troublesome and stressful, and as I said, I lost the whole of the site and had to start from scratch.