Your eye doctor
is the best person to discuss this issue with you. There is a very legitimate reason for discarding the contact lenses
at the end of the recommended two weeks. Briefly, when you wear your lenses, they are developing deposits of proteins and other substances on their surface. Over time, if these deposits are allowed to build up, they can lead to eye irritation or predispose to serious eye infections.
The exact amount of time that is required for these deposits to build up to the point where the lenses need to be discarded depends a lot on the exact chemical composition of your brand of contacts and also on the type of disinfectant or cleaning solution that you are using for the lenses. In your case, this seems to be two weeks.
I would recommend discussing the issue with your eye doctor the next time you see them. If you are interested in wearing the contacts for a longer period of time, then it may be possible to switch to a different brand or type that allows for longer wear. Longer wear contacts tend to be more expensive per lens, but overall the may be cheaper in the long run, and your doctor can help you decide which option is best for you.