No longer a 5-speed transmission

My 2000 Mirage (with 145,000 miles) no longer stays in 2nd gear. Due to the age of the car I do not want to replace the transmission but I would like to get a few more months out of the car. For now I am just shifting from 1st to 3rd. My questions are; (1) Is there anything I can do short or replacing the transmission to get 2nd gear back, (2) if I don’t do anything to fix the transmission is there any reason I should not continue skipping 2nd gear until something else breaks and (3) is there anything I should do like flush the transmission to try to extend its life?

Manual or automatic? You can’t flush a manual transmission and it would be a waste of time on an automatic with that problem. Keep doing what you are doing until you hear a better idea.

The syncronizers are shot for 2nd gear. Removing and rebuilding the transmission is the only option to fix it. However, if the gear lube has never been changed out, maybe changing the gear lube will save what is left of this transmission. Gear lube has a service life, and 11 years plus 145,000 miles is well beyond it. I generally use a 5 yr or 60,000 mile limit on gear lube unless told different. My wife had a 4WD Suzuki that wanted 30,000 mile change of lube in the front and rear diffs, transmission, and transfer case.

The problem is more than likely going to be a worn 1/2 shift fork and/or worn sychronizer hub assembly.
The wear could be due to a lot of 1/2 shifting in city traffic and wear caused by resting your hand on the gearshift lever, which is a habit that many people have.

There is no cure for this problem short of tearing into the transmission and at that mileage would involve a complete, and expensive, rebuild.
Just continue shifting from 1st to 3rd. This will not harm anything.