It will be a little work but should clear up the problem. Remove the plant from its pot, hose off soil, repot in sterile potting soil (no perlite), water well to settle roots back in (if this is not done air pockets will form around roots and with no moisture will die). Here are some tips for re-potting:
***Moisten new soil before using. It is much easier to work with and to water moistened soil
***mix soil with peat (which should be moistened before hand as well). peat helps keep a more sterile environment and retains water so you will not have to water as much. Peat is a non-renewable resource so not one I recommend or use much but sometimes it is called for.
***put small stones, gravel, broken pieces of clay pots or styro peanuts in the bottom of the pot for drainage. This is a MUST for plants in high humidity/soggy environments. the styro peanuts are used only if you are using a large heavy pot to make it lighter. the others are better drainage.
***regardless of pot size do not fill with drainage material more than about 1/4. the plant roots need plenty of soil to grow.
After you have repotted your plant I would leave it out of the cage for a few days, let the top inch or so dry and then put in cage.
hope this helps! Sorry that it may seem like a pain, but it is that or fungus gnats!
lele
p.s. about those peanuts...make sure you don't use the type that are made from cornstarch as they will dissolve. LOL! 
Here is a fact sheet on fungus gnats
fungus gnats
-----
0.1 veiled - Luna
0.2 house geckos - Gaia & Tia (both MIA 
0.2 felines - Kyndra and Líta
1.0 African Clawed Frog (for summer)
0.5 Mad. Hissers (for summer - all girls, no little ones, whew!)