I would like to add that the Libyans take your passport when you arrive in the country, give you a card as expat, and give your passport back when you leave the country after one month (or when you fly). That means that you ARE NOT ALLOWED TO LEAVE THE COUNTRY in between even if you have days off.
If this is the case then this restriction is imposed by Afriqiyah and not the Immigration authorities. I used to work out in Libya (not for Afriqiyah) and due to the fact I was crew, I had my visa stamped to allow multi entry/exit. Such a stamp is rare but it is available.