Codes are 170 and 171, check engine light continues to come on?

Hello, it sounds like you have a vacuum leak, the P0171 is a lean air fuel mixture code and the P0170 is a fuel trim issue which is what the engine computer uses to correct fueling issues. The reason the check engine light comes back on after a battery disconnect is because you're temporarily erasing the ECM memory and after a drive cycle it is seeing the same issue. Vacuum leaks can be the intake manifold gasket, any one of the vacuum lines such as the Purge valve hose, it could be the purge valve stuck open. That would usually set a different code but not always. Also, after you find the vacuum leak, I would do an oil change as well. Vacuum leaks cause the engine computer to compensate for the "false air" coming into the engine and it adds fuel to the mixture. This will contaminate the oil faster. Tell your mechanic to use a smoke machine to help find the leak faster. instead of replacing parts, the lean mixture is most likely causing the other code. Here are some guides below, I'm not sure what you mean by the computer saying there is an electrical problem, the vehicle just needs to be properly diagnosed. If you have a scan tool that can read live data, look and see what the Long Term and Short-Term fuel Trims are. They will tell you how much the engine computer is compensating for a problem.
One other thing, these Hondas need a valve adjustment every 30,000 miles, it is a very easy procedure, but they are one of brands that absolutely needs this to be done regularly. Tight valves cause all kinds of issues, so do valves that have too much play in them, Tight valves do not seal the cylinder completely and valves with play in them do not open far enough, this can wear the camshaft's lobes out quickly.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

https://www.2carpros.com/articles/7-common-symptoms-of-a-vacuum-leak-in-your-car-how-to