Mitsubishi Repair Problems? Ask a Mechanic for Answers ASAP
The CD player is almost completely self contained on this model... so any problem you have with it will just about always result in replacing the cd player... there are no owner-serviceable internal parts, though there are low level electronics companies that can repair these.
The only thing I would do is just make sure the face plate is not getting in the way. On 06-07 models we used to see alignment issues where the faceplate would cause the CD to go in then eject right back out (though it would not cause it to suddenly eject like yours did). To check this you would simply pull the face plate off (no tools, it just pops off), the remove the philips screws holding the radio to the dash and jostle the radio briefly. Then temporarily install the face plate and see if it takes the CD in again like normal. If it does, it is just the alignment and you can bolt the radio back down and should be fine.
If the problem persists though (which again with the cd suddenly ejecting unannounced it probably will) then that would only leave you with an internal issue to the radio.
If that happens and you want to keep your original radio, I only use H and R Radio (located in PA, but they are mail-in based). Be aware though that low level repairs like this are usually a bit pricey. The cheapest I have gotten a radio back from H and R is about $250, and they are one of the cheaper reliable repair shops I have found. If keeping it original is not that important you can usually find these radios on ebay or salvage yards from $25-100 (depending on single or 6 disc variant), and would be more cost effective as long as it has guarantee on it so you know you won't get a dead one.
Unfortunately these do just fail sometimes. It could be completely out of nowhere, in some instances we will see a failure right after driving down a bumpy road and something got jarred loose. There isn't really anything to blame for it, it is just the way it is unfortunately. As long as the disc is OK (I'm assuming it was fine since it had been in there previously) there is only the internal condition worry about. E01 is just a system focus error... meaning it can't see the disc properly. But of course if it is not fully retracting the disc that is going to happen.