Powerstar ae-125 takes forever to warm up and gets cold during shower

Shower heads have flow limiters installed in them. This means the water heater cannot sense the water flowing and therefore it wont come on. Take the shower head off and look in the end for a piece of plastic that is in the swivel. Remove it. Then put the shower head back on.

http://waterheatertimer.org/pdf/Bosch-AE115-AE125_manual.pdf
Bottom page 10 troubleshoot

Add tempering tank to pre-heat cold incoming water
http://waterheatertimer.org/Tempering-tank.html

Call service technician

Delime heat exchanger.
http://waterheatertimer.org/How-to-delime-tankless-water-heater.html

Replace with tank type?
http://waterheatertimer.org/How-to-install-electric-water-heater.html
Gene

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

Copy following link:
http://waterheatertimer.org/How-to-wire-Tankless-electric-water-heater.html
AE115 has two elements and requires two 40 amp breakers.
A#125 has three elements and requires three 40 amp breakers, and is considered 'whole-house'
Do not install a tankless water heater because they cost more to install, and cost more to operate and maintain..
Add a comment and ask question.

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

This is a "point of service" tankless water heater that was manufactured by BOSCH. BOSCH is now Bosch-Climate.us. Technical support is available at 866-330-2729. P.S. check this site: http://tanklesswaterheaterz.com/bosch-ae-9-5-powerstar-1-5-gpm-point-of-use-indoor-tankless-electric-water-heater-reviews/

Problem might be crossover from failed single-handle faucet cartridge:
http://waterheatertimer.org/Crossover.html

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

All resets and breakers trip with high heat.
Do you mean the tankless unit is tripping the 40 amp circuit breaker?
Or the thermal cut-out, located on unit, is tripping?

Is this a new installation?
Or was the tankless working before and stop working?

Copy following link to check wiring.
AE 9.5 requires 40 amp breaker and 6 gauge wire.
http://waterheatertimer.org/How-to-wire-Tankless-electric-water-heater.html

If the unit is tripping the thermal cut, -out, then product manual says to call Bosch or service technician.
Call Bosch 866-330-2729
http://waterheatertimer.org/pdf/Bosch-Powerstar-AE3.4-7.2-9.5.pdf
Thermal cut-out can trip if water flow is too low.
Try changing power selector screw from Hi to Lo so only 1 element is ON. See diagram page 6 of manual.
Adjust the 'outlet service valve:' The manual recommends that a ball valve be installed between hot outlet and faucet. Adjust the valve so more water flows to faucet.
Remove aerator, clean aerator, don't use low flow restrictions or low flow shower heads, replace leaky faucet cartridge on single-handle faucet.

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

Any suggestion could include a list of possible problems from bad PC board, burned out element, bad sensor, loose wire, or combination or these.
More information is needed to make a guess.
Test elements for continuity.
Check wires for loose and burned connections.
Open TP valve and test if hot water is available at machine.
If water at TP valve is hot, then problem might be plumbing-related, for example crossover.
http://waterheatertimer.org/Crossover.html

try bleeding that section of pipe. or the whole system if not.

Ok, sounds like a flow sensor issue, is your house water pressure steady or does it fluctuate? The sensors on these seem to be a common issue and this model has many issues with heating. take care

good luck,, there aren't that many whole house electric tankless units of any kind even made