****NOTE*** Xboxs with version 1.6 motherboards CANNOT do this and do not have to look for it either. Only other versions.
If you are experiencing trouble with your xbox resetting or other problems related to clock settings than this is something you should do on your xbox right away.Even if it is working properly you should inspect and remove this component asap.
One very good thing to do would also be to replace any and all other leaky caps on the board when you open it up clean out the disk drive and lubricate it. Put new fresh thermal compound on the cpu and gpu and REMOVE the clock capacitor located in the bottom left corner near the controller ports. It is a capacitor marked 2.5v 1uf and is the root of the lack of the clock time working in your xbox. Although this could be replaced and even modified to fit a coin cell battery, the first thing should be to remove this old cap from the board.
After removing the cap, what will happen? The answer is you will not notice any change from before except that every time you start up your system it will say to input the date and time, something the system does already as it is.
What happens if I leave it in? you will risk having the leaky acid eat through your motherboard and destroy the system eventually
What do I do if I see leaky acid or white/green color liquid around the capacitor? First remove the capacitor (2 ways shown in the video) then, using a q-tip with some Vinegar or Lemon Juice on the end, wipe around the affected area several times and let dry. After, test the system. If everything works out ok then you are set, if things are not changing than you may have a couple of eaten traces and will need to patch them.
Hopefully this will help you with keeping your xbox running a bit smoother for a little bit longer.
Big thank you to iDavidP for mentioning this subject as it can be easily forgotten and an unknown secret killer that destroys your xbox.