I had a similar problem with my SST-7's, but it was the slide sole instead of the heel. They had a lot of miles on them anyway so I just bought a new pair of SST-6's.

You could probably replace the velcro though and get more use out of them.

Thanks so much for your replies. I think I will order a new pair of shoes at this point.
I will probably opt for the SST 6's over the 8's since it appears that some reviewers
have had some issues with the sliding toe (tip).

I've currently got SST5's and have this issue with one of my slide soles (happened to be my most used/favorable sole ).

It wasn't the shoe, but the sole, as all other sliding soles velcro on nicely.

I'm not a fan of the 8's and was informed by Dexter via FaceBook that a new model will be coming out "soon".

I've ventured into overseas equipment and recently picked up these (haven't tried em yet) where the bottom soles look like swiss cheese with holes, and in those holes you can fill with other slide pieces (example. slide sole - 4, front hole - 6, side holes - 8, back hole - 3)

They look like a combination of the Linds Exxxtra,
http://www.linds.com/exxxtra3_lrg.html
and 3G Tour Ultras,
http://www.900global.com/newglobalshop/wp-content/uploads/2014/05/3G-SHOE-POSTER-2014.pdf

I tried a new heel but unfortunately, it too, would not stick. I also tried another heel (one that I rarely use) with the same results. This "stiction" problem appeared to happen practically overnight. This is what led me to believe that perhaps it just needed to be cleaned. In addition, I rarely change the heel that I most often use.
The shoes are not that old. I have had Dexters for years and they have all worn out over time, as will any pair of shoes, but this is the first pair where the Velcro failed on me.  I appreciate all of you who took the time to offer your suggestions. I don't mind the thought of purchasing a new pair if this problem is limited just to this particular pair of shoes. I have been more than happy with Dexter over the years.

Thanks so much again!