When canning, you're going to experience some sealing issues. (see Crying Over a Broken Seal) I don't care how accomplished you are at canning, it's gonna happen. There's a multitude of things that can affect a seal. Very often, you can re-process the item or freeze it for later.
Let's cover the items that aren't good for re-processing, first. It's difficult to re-process product that requires a long processing time. Items like soups, stews, beans, veggies; will all turn to mush if they go to 240 degrees for however long a second time. Alternatively, I wouldn't want to run a low-acid food through the waterbath for 3 hours a second time either. I usually repackage and freeze these types of products. About the only thing that I pressure can that I WILL go ahead and re-process due to a bad seal is broth. (Very often, I re-use lids when canning broth and if one of those seals is bad; I can re-process the broth easily.)
Waterbath short processing time items are ideal for a situation of re-processing. Jams, jellies, fruit butters, fruit in syrup.... etc. I made some pie filling last week and had a jar not seal. It was simple to refill another jar with the product, put on a new lid and ring and send through with the next batch to get a good seal that time. Very often, you can tell shortly after the load comes out of the canner (within an hour), that a jar is not going to seal. The whole 12 hour crap is just that, crap. I firmly believe that leads to false seals and failed seals later on. Why not nip it in the bud right away and re-process?
How to re-process product:
Identify the jar that hasn't sealed.
Check over a different clean jar (are there any nicks or cracks) and empty the product into it.
Heat up a NEW lid and a fresh clean ring and use them for the new jar.
Process along with the next batch (using the same processing time) in the canner.
Usually this results in a good seal.
What are the causes of jars not sealing while processing? For me, it is usually a nick in the rim that I didn't catch the first time OR I've re-used a lid one too many times. There's a laundry list of things that can go wrong. Was the ring tension too tight or too loose for the brand/type of lid that you're using? Was the pressure canner brought up to temp way too quickly and caused siphoning? Was there enough head space inside the jar for the food to expand while it cooked? (Pie filling is notorious for this.) I'm sure there are some instances that I'm not thinking of.
Food preservation techniques are skills worth knowing and knowing how to correct problems is part of that skill set. If somebody asked me how to run a dehydrator, I would be flummoxed. You have to learn as you go!
What items have you had to re-process or freeze lately?