Mine started doing this during the summer after some significant knocks. It doesn't seem related to the batteries; I've tried different kinds - does the same with lithiums - and padded out the batteries until I could hardly get the back on; it still faded out after a short while.
I emailed Garmin claiming this was a fault as I have only used it on road and MTB handlebars which surely shouldn't be enough to cause an internal fault:
Unit switches offwhen knocked
I have used my Etrex Legend HCx on a Garmin cycle handlebarmount for approximately 18 months without issue. Recently, the unit is losing power when a significant bump or pothole is hit on the road. Sometimes the power drops instantly, others the display fades out like it still has power but something internally has shook loose. I have tried different batteries, including NiMH rechargables and Lithiums, in case it was a particular set that was undersize and moving in the unit, but even with a small amount of tape around the batteries to make sure they are very snug it still does the same shutdown on a significant bump.
This was the disappointing reply:
Thank you for contacting Garmin Europe.I am sorry for your difficulties. Unfortunately we don't do repairs,however we do have a replacement service instead. You can send your unit to us to be replaced with an as-new refurbished model with a fullyear warranty on it at a cost of £56.66 GBP inc VAT. Unfortunately we are not able to offer an upgrade or part exchange. If you would like to do so, please call us on 0808 238 0000 (walking and fitness) with your credit card details and unit serial number.
So the solution is to send you unit in, pay half the price of a new one for a refurbed unit, then they'll fix yours (something they claim they don't do) and sell it to the next guy for half the full price as well. Sounds like a nice money-spinner for them.
I thought Garmin were like Hope (for example) in that they were excellent at aftersales. The message I've got from them is ~ 2 years is the expected lifetime for an Etrex in regular use on a bike.