A Solution:
Take a mint or some other candy. Take these and suck on them at the same time you suck on chew the gum and the flavour should come back. Also, take the candy and smash it into pieces and introduce that into your mouth or cover the gum with it.
Adding a drop of some flavoured syrup also helps. Or even chewing on mint leaves, but do this on a different side of your mouth. Otherwise your gum will be ruined.
Chewing the gum slower helps keep its flavour more, as the saliva that is breaking down the flavour cannot circulate through out the gum as fast. By chewing you are kneading the saliva into the gum.
And there is no way to stop it, it appears.
wonderopolis.org
So why don’t these flavors last? When you chew gum, the saliva (spit)
in your mouth begins to digest the sweeteners and flavorings in the
gum. Unlike the gum base, the other ingredients can be broken down and
digested.
As you swallow while you chew, the digested sweeteners and flavorings
move through your digestive system to your stomach. Eventually, you
digest all the sweeteners and flavorings, and all you’re left with is
the gum base and softeners. That’s when you sense that your gum has
lost its flavor.
And something I haven't tried.
Barry - Yes. So Martha’s been chewing some minty chewing gum and I
hope by now the mintiness has disappeared.
Martha - Yes and it’s going a bit cardboardy and generally not very
nice.
Barry - OK. So now what I’m going to do is I’m going to ask you to
take it out of your mouth and roll it in this little mound of icing
sugar that I’ve got in front of you and if you just pop that back and
have a chew on it.
Martha - Urgh, choking on some icing sugar.
Barry - Tell me how it tastes now. Just keep chewing away for a
moment or two. So what we’re really investigating is the way that one
sense has an impact on another. So, here we’re talking about how taste
might affect smell.
Martha - Mmm…Yeah, so it’s definitely tasting newer again and yeah,
the mintiness is coming back.
Barry - So the mintiness has come back and that’s amazing because
there is no mint in icing suger. So that’s a strange effect. What
you’re getting is the fact that when you combine the sugar with the
odour in your mouth, you get something super-additive that’s more than
the sum of the parts. You’re not getting them both together, you’re
getting the sugar boosting your ability to detect mint and the mint
seems to resume its presence.
So apparently rolling the gum in sugar may help.
Additional Info
Wikihow: Make Chewing Gum Last Longer: Put the gum in cold water for a time(I wouldn't do this for very long) and this is suppose give it back the original texture.