I found a WEB page that, among a LOT of other things, talks about troubleshooting your type of garage door opener as well as others. Trouble is, the WEB page is 704K!!! I have no problem loading it because I'm working on a T1. If you have access to it from a 'slower' connection, it may take a while to load. But once it does, you can do a page search for the word 'genie' (w/o the quotes). The 2nd or 3rd 'hit' on the page talks about troubleshooting the remote. The WEB page is set up such that, if you were to scroll up a little from where you find the word 'genie' you'll see the question a person is asking. There are a few suggestions with some detail and I can get your mind going here. The WEB page is:
1) If you have a 2nd remote, does it have the same problem? - If not, compare the antenna wires and see if they're in the same condition. 2) After 2 years, would it be unreasonable to assume that the remote has been through some abuse? Like dropping, in the sun, getting wet, etc., etc.. 3) If the remote (or the opener) has a transmitter signal adjustment on it, check the instructions to see how to 'tune' it.
You can take a chance and go buy a Universal Remote to see how it works (if you only have 1 remote in all), and see how it does. Be SURE it's rated (or even compatible) to your Intellicode. If not, there are a few sites on the WEB that sell Intellicode replacements at a decent price.