Over flow leaks constantly after 8 years, never done this before. What should we do?

your not making sense with you question --state it goes cold in middle of shower --but state it will stay hot or cold forever ----if its the latter continued hot till you shut off water that normal working if the unit shuts down during shower then you have a problem ----unit is set at one temp and runs at that temp and you use shower 1 handle / 2 valve what ever you own to adjust temp their are really only 4 reasons stops making hot water ----2 are usually well water supply --incoming water pressure /flow or to cold ----other are gas valve -or sensor so i would look into your shower handles since almost all have adjustments and anti scold safety

Check to see if you have any leaks in the system, check the Foot valve, or check valve.

1) Bad gas control thermostat, or thermostat has come out of calibration, or water leak running hot water out of tank.
Turn up temperature.
Replace gas control valve.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent
http://waterheatertimer.org/How-to-adjust-temperature-on-water-heater.html

2) Clean air intake, put ear against pipes and listen for water leak, check that flame is clear blue and that combustion gasses are flowing up the vent pipe and not blocked.

3) Call service technician.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Put a brass garden hose cap over the dripping drain valve.
Call the plumber.
Absolutely the plumber should take care of this for you since the cap has to be tightened pretty tight.

See illustration:
http://waterheatertimer.org/images/drain-with-cap-500.jpg
http://waterheatertimer.org/How-to-replace-water-heater-drain-valve.html

Comment back and let me know what happens.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Change the expansion vessel sounds as if its leaking somewhere

If you are on city water and your inlet to your house has a back flow preventer this could be you problem.if so theres an expansion tank that can be installed on the cold water line,after you water warms up theres no room for expansion and the relief valve goes off at 150 psi

Check to make sure you haven't any leaks any where. you may have a leak somewhere or if it's recirculating the water in the unit itself.

possible problems not knowing age of unit the
control valve could be sticking open allowing gas to continue to flow until high limit is reached and shuts down valve another possible problem with the newer style back flow preventer being install by water companys the rapid heating and expansion of the water over pressures the water system causing releif valve to pop open and reclose most water heater manufacters are recommending instalation of an expansion tank to allow the growth in volume of water somewhere to go is valve constantly leaking or only during heating cycle if you could supply additional information does unit only leak when heating
or is steam expelled when releif valve opens
t-stat not opening gas valve sticking partially open
bad high limit bad pressure releif valve no expansion tank to allow for thermal expansion if steam is present and unit is boiling water inside replacement of water heater for safety concerns,would be reccomended if only water and pops couple of times water temp not over 140 degrees after most hot water has been used out of tank and is reheating most of capacity probably lack of expansion tank as the releif valve is the final safety device on a water heater is of great concern
the temp control gas valve or high limit are supposed to shut unit done long before the safety limit of releif valve is reached

tankless water heaters are a great appliance with one small draw back they require a constant flow of water through them to maintain production of hot water if the water presure fluctuates they can cut out momentarily or if your water supply is less than great ie hard ,high iron,
sulpher ect.. then the heat exchanger can become plugged over time like say 5 years. Contamination of the flow sensor/presure switch could also be a culprit depending on how handy you are a through cleaning with a good kettle descaler will probably help.
Good Luck