I have a prestage remote starter, my car is 2008 ford explorer, after a few days my car will not start, it makes a clicking sound

Why didn't the mechanic continue on & resolve the issue?

You don't have the experience to do so, as your here

No one can tell you what is wrong without the vehicle to test,
common sense

Either your starter or battery

sounds like a problem with the starter, i had the same thing happen to me when i took the starter to get repaired the guys to me i was losing the voltage in the starter they installed a relay on the outside of it charged me twenty dollars. that was a year ago haven't any more problems. hopefully yours will be that easy.

got a 2004 ford explorer it wont start but it turns over put fuel pump starter evap canister and purge valve it was broke,and a battery fuel filter,tac system and it still wont crank

Fords usually have a starter solenoid separate from the starter. If the contacts are bad in the solenoid it will make the clicking sound. Replace the solenoid and it will start.

First, try a new battery or charge a known good battery up and install. Make sure the connections at the battery and the starter are shiny and clean when removed. Do an amperage draw test to see how many amps it draws when trying to start (click).

If the amperage draw is 80 to 120 Amps and it doesn't turn over vigorously, the starter is bad, but the connection is good.

If the amperage draw is only 1 or 2 amps and it doesn't turn over, then the soenoid on the starter is bad, but you would change the starter and solenoid together as a unit to repair.

Good luck on this repair.

It might be your anti-theft alarm system. When the car doesn't start, is there a ticking sound inside the car? If so, hit the unlock button a few times on your keyless entry remote, until the ticking stops, then try to start the car. Hopefully this helps.

You should definately replace the battery. It is probably battery acid gas you are smelling. Eggy or sulfury?

P.S.
Check you positive side cable for corrosion and you might need to replace the cable because it runs from the battery direct to the starter and to the starter relay that is mounted on the right front fender under the hood. You have 2 (two) starter relays on your Explorer.

The clicking sound could be the sound of the silenoid trying to activate a bad starter. See the bendix moves in and out pushing the gear into the flywheel. The starter itself turns the flywheel. So they are a working combo. You sound like you may need a new starter. Here is a tip. Buy original equiptment or get the same one rebuilt buy a shop. Many alternator and starter shops (even tractor repair shop) can handle this type of work in less than a day.