I know precisely what your problem is. I had it occur on a Symetre and a Sahara, both older models. If you remove the spool, you'll see a hex nut on the shaft. Loosen that and take off the top of the reel. Underneath you will see a large rubber ring that supports the reel head that the spool covers.

Chances are that it is worn out. Inexpensive to replace and once you find the part number on the particular reel model you have, you can google Shimano Parts and you'll find plenty of good suppliers. I got mine in like 3 days and it wasn't expensive.

It is a design flaw and from what I gather, it's been corrected with the new models. Which is why they kicked up their price by $20.00 on all their reels! Another reason why I'm now favoring Pflueger Presidents.