Water does not stay hot it is uneven in shower, from cold to hot then hot to cold

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

Test for crossover, where bad faucet cartridge or recirculation check valve keeps hot from reaching taps
http://waterheatertimer.org/Crossover.html

Add a comment and say what you find

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

This should run two showers at once with no problem. If you have a shut off valve on the cold side of the heater, try closing about halfway. This will slow the water flow and the water will have more time to heat up as it pases through the tank. If you dont have a shut off valve, just cut back the hot water valve on your shower and do not use any cold water. If it gets too hot then turn on a little cold water. The object is to slow the speed of the water going through the tank. Tankless heater take a little getting use to but they work great when you know how to treat them. On my shower I turn the hot all the way on until it gets hot and then add a little cold water to bring the temp down. You may have too much water going through too fast to be able to heat it up to what you need. Try this and see how it works.

Problem new or old? How long you have unit? Sounds like not enough flow to keep burner on. Tankless need at least .6 gpm to keep hot water flowing or else the burner fires then shuts fires then shuts and you get a sandwich effect...hot cold hot cold. If you have new diverter valve in shower -vs- old two handle type try turning hot water ALL the way ON and see if hot stays hot. If it does stay hot then slowly adjust to cool and see if you maintain a good MIX for proper temp. If it goes cold again try this......LOWER control pad setting to a comfortable 105 degrees (ladies) 100 degrees(men) and turn shower valve all the way to HOT. See if your temp remains consistant now and if it does then problem solved. Tankless mindset...set temp on control pad and stop trying to MIX at shower valve. Thats how these things work. Thats why I install a control pad in each bath and one in the kitchen for adjusting ash temp during dishwasher on time. ditto for wash machine. You should never need to turn on cold water if your unit is set to proper temp at controller. Hope this helps

How long has the heater been installed?

Does it happen to any other fixture? If not, it's most likely your shower valve and not heater.

it is because the tub has a temp control valve in it so if you were to put more cold with the hot it will last longer but still won't be all the way hot,, now a days people are suing the manifacture because they are getting burned form the hot water so they put these saftey temp controls in place of the old style 2 or 3 handle faucets,, there fo no more real hot water nothing you can do outside of change to the othere type of faucet 2 or 3 handle tub shower diverter,, that why the water is hot in the sink but not the tub.....

Will the water stay hot in the kitchen sink? Try to isolate the problem. If it is happening at all hot water locations, then it will be related to your water heater. If just in the shower then it is related to the mix of water ratio coming out of the shower hear. If its only the shower, then you are getting too much cold and not enough hot through the pipes. This can be very simple to fix by replacing the handle going to the shower. If this does not work then you may have a problem in the hot water pipes. After you isolate the problem, please post another question here.

I found a way to get warm water in the shower, but I'm not sure it qualifies as a solution. After trying everything else I thought that maybe when I was feathering the faucet in the shower toward the cold side so I would get warm water that at a certain point it blocked the flow on the hot water side enough so that the sensor in the hot water heater sensed there was no demand in the line and it shut the water heater off. To test this, I went to the kitchen and turned the kitchen sink faucet all the way to the hot side and then turned it on so that I got a small flow of water. I waited for the water to get hot to be sure the hot water heater was working. Once it was hot, I left it running to keep demand in the line and then I went to the shower and turned the faucet on. When the water got hot I started feathering the control towards the cold side and soon I had warm water. So I think I'm right in that the sensor in the hot water heater was shutting the water heater off when the demand in the shower was lowered to a certain point when I was trying to adjust the water temp in the shower.

So now I can get warm water, but it means I have to leave the hot water running at another fixture in the house to create a false demand in the system so the hot water heater doesn't shut down. Is there a way to adjust the senor in the hot water heater so that it will stay on when I'm using the shower only, so I don't have to waste water by running another faucet when I want to take a shower?