You can inject epoxy under the reel seat, but it is a temporary fix at most and will be messy. Any epoxy that you can thin well enough to inject is going to leak out all over the place during curing, unless you continually keep an eye on it. Realistically - it's a band aid for the problem and not a permanent fix.
You have a couple of options to choose from.
1) CAREFULLY cut away all forward cork from the rod. Go slow. Don't cut down to the blank right away. After you get most of the cork off, use some sandpaper to get the remainder of the cork and glue off all the way to the nice smooth, non nicked up blank (important). After that, the reel seat will slide forward on the rod, and off of whatever bushings were holding it in place from the factory. The bushings could be anything from graphite to cardboard. Take a good look at them and determine if they are serviceable. They probably aren't. If they are in bad shape, remove them. If in good shape, make sure they were giving the reel seat a fairly snug amount of support (they probably weren't if you could rotate it on the blank).
OK... now for the repair - This isn't my favorite way of fixing it, but if you aren't ripping the whole rod apart, this is the best solution. Before you start - get the reel seat bumped up to the cork so that the guides and seat and in the right position. Mark both the cork and reel seat so that it will be situated correctly when you are done. Use 1/2" to 3/4" masking tape to make several "bushings" for the rod seat to slip into. There should be enough room under that reel seat to put at least 3 or 4 bushings, depending on what kind of seat it is. After you get each bushings on there, starting from the cork handle end and testing each one, and when you slip the reel seat on top of them, it should be nice and snug (important), then slide the reel seat forward again and make sure none of the bushings were damaged when you put the reel seat on. Then you are going to need some epoxy. You can use some regular two-part liquid epoxy, but it's hard to keep in place over such a large area. It goes between the bushings, as well as on top of them. This is why I use a product called U40 Rod Bond. It's a two-part paste that works wonders for things like this. Slide the reel seat quickly in place and watch the epoxy squirt out at the cork end. Have something ready to clean it up. Let it completely cure. Then you have a choice to make in front of the reel seat - you can take cork rings, split them in half and ream the centers, then epoxy them in place in two parts, sanding them to size and shape after they dry for a foregrip replacement (time consuming and difficult to make look right), or (my recommendation) - use some rod wrapping thread and make a trim wrap in front of the grip, leaving it completely off the rod.
2) What I consider the "Proper way" - Strip off all guides, remove the foregrip cork and reel seat. Prep everything on the rod (light sanding to remove old epoxy, etc... as above), clean out the reel seat interior of all old material / epoxy or replace the reel seat. Use graphite arbors vice masking tape for the reel seat bushings (http://www.mudhole.com/Shop-Our-Catalog/Arbors/Graphite-Arbors-FA) Repair everything as above instructions, but you get to put the foregrip back on in one piece and have a better foundation for the reel seat that gives you more sensitivity.
3) Find some liquid epoxy that can be injected under the seat and use a syringe to get it in there. It's going to be tough to get it anywhere other than the ends. It won't last long, but it might get you through for a while.
All the best,
Glenn
