Most UDRPs are heard by the WIPO or NAF.
From my experience UDRPs Filed in the US tend to be heard by the NAF and European, Australasian cases are through the WIPO.. however this is not always true for all.. just the ones I have been involved with.
The simple fact is.. UDRP should be worst case scenario. Too many companies send angry threatning letters DEMANDING that you transfer a domain to them.. Even though there is no law that says just because you have a trademark, entitles you to the domain name.
Sometimes a nice polite email explaining the situation avoids huge costs for both parties.. and its a little less stressful..
Recently I had a company president demand a domain name that I have owned over 2 years.. He insulted me and made threats... I responded very professionaly an politely and explained how I came about the name..
After about 3 days and 20 emails a UDRP was avoided and I was well compensated for the domain.
You catch more flys with honey than you do with vinegar.
However back to the question at hand.. if the respondent to the UDRP who won the case then goes on to use the domain in bad faith in order to disrupt your business then you should have rights to reapply. (I can not confirm or deny this you would have to seek a TM lawyers advice on this as its not that straight forward)
Just monitor the domain.. take screenshots.. build a case against them..
If all else fails.. I know a big guy called Moose