I agree with other posts, you don't lose eligibility unless you let a non qualified borrower assume the mortgage. If a qualified veteran assumes the mortgage, he can lock in your interest rate and as long as he qualifies as a vet you can get your eligibility back. If you sell it to a civilian its yours because the VA isn't backing a conventional mortgage. I am on my second VA loan and I agree there are many positives. No down payment, no PMI are the big ones. They have a streamline re-fi deal that is pretty good. Up until recently if the rates come down its just drawing up papers and closing. They never even needed an appraisal or even a credit/job check. Just as long as you were making your payments you were good to go. I hear its still good buy they may require an appraisal now.
Some cons are: The funding fee's. I believe the first purchase is relatively low, 1.5% or so if you were active duty or activated. It goes up after that, so depending on how much the house costs, you may be better off with conventional. Also the VA sends in their own appraiser and can deny the loan for a lot of silly reasons. An example is unfinished projects. I had a friend who was denied because the house he was looking at was only 1 year old, but the walls in the garage were formed up for drywall. The unfinished walls put the kybosh on the deal. Our first place had some peeling paint on one side. We arranged to have it painted and then it was approved. So no fixer uppers for the most part. Also a while back the underwriting was a pain in the a$$. We closed the day after closing because there were 3 underwriters for the entire system, and that was with a 120 day notice. They have a much better system now, it's automated for the most part.
Overall a good deal though and you can apply for a VA loan through any decent mortgage broker.