Nope. If the landing permission expires, then your re-entry permit is expired. The visa can be something as basic as a single entry. Mrs. Pickles had a 1 year dependent visa, which in theory she could have used to come in through the visitor line for a year. The first time she left Japan, she was forced to buy a re-entry permit because her landing permission was for 3 years even though her visa was for 1. It turns out the immigration officer was in the wrong, she could have come in and out in the visitor line for a year with that visa.