We recently have gone back to using our Garmin Legend for caching. It had sat on a shelf for a few years as we used newer models we had access to, but these are no longer available.
Our Legend had worked wonderfully for many years and many finds, but now has been giving us erroneous readings, like GZ at 350′ off a railway bed state trail, a couple of hundred feet away from a tree hide on the edge of a clearing, etc. Weather conditions and tree cover don’t seem to be factors, this has happened several different places and days.
I suppose the answer is yes. It is not exactly wearing out, but it is always possible for a circuit board to go bad. I would suggest you try a hard reset (allow the settings to go back to factory settings as well), and see if it gets better. If not, contact Garmin support, but my guess is that you can buy a new etrex for less than it will cost to fix the one you have.