I have not read the comments on this post (kind of busy at work).
I have actual experience in this topic. I dated a girl for a few weeks and then we decided to end it for whatever reasons we had. About two months later, after talking it over with mutual friends and my mentor, we decided to get back together. It still did not work out, but we are friends now and there is no animosity.
(Some of) The advice that I was given when I decided to date this girl again was that I can’t just date her for one or two dates. We had to go out for a couple of weeks, to really make sure that we are for each other or not (even if we had new issues with each other we should discuss them with each other and work them out if possible, not to keep them “bottled up”). This would then preclude us from having to go through the whole scenario again. Also, it was advised to us that whatever problems we had with each other the first time around we had better make sure that it was resolved or else it will be fruitless to go out again.
I would pass this advice onto whoever decides to go out with a girl/boy they have already dated.
Personally, if both the girl and boy want to go out with each other again after they broke it off once, they should. But make sure that whatever issues were on the table the first time around are resolved, or else you will just be going through the motions again.