That is definitely a possibility, although there is also the problem of O2 ingress as the cork degrades.
IIRC, Chateau Laffite Rothschild sends a team around the world every so many years, and they will test CLR wines over a certain age. They use a very fine needle to withdraw a small sample and test it, and will recork bottles and provide a certificate of authenticity to go with the new cork.
If you are concerned, recork your old wines with a fresh cork. Do NOT wait until you find a problem -- at that point you're too late. It's like re-roofing your house -- if you wait until you have a leak, you've waited too long and have bigger problems. If you are a afraid of a problem, for the cost of a few corks, recork the bottles.
For most people, the problem is that most wines won't last 10 years, they'll reach the end of their life and start to decline. If your wines have reached age 8 or 9 and are doing good? That is seriously cool!