We have been experiencing reduced water pressure on the hot side, affecting all faucets. Cold is fine. I have flushed the water heater and confirmed good pressure going in there and on the whole cold side. I tried using a small air compressor to blow air back through the system with the water heater drain open, but still have the problem. When I initially open a hot-water faucet, the pressure seems okay for a few seconds and then begins to slow down.

The water heater does not have disconnects - only the shutoff valve for the incoming cold water.

Any thoughts?

You say all fixture have poor pressure so we can skip checking individual hot inlet ports on cartridges for now. Try the drain spigot at the bottom of the tank, come back and tell us how that pressure looked.

There is good pressure at the spigot on the bottom of the heater and the water flows clear. I turned the burner off and drained it down and then refilled. Same issue.

Draining a water heater is not flushing a water heater. To flush you leave the burner on and the main on full. Allow the incoming water pressure to flush the tank. Since you say the pressure is good at the drain spigot it is likely the nipple or heat trap at the exit of the hot line on top of the tank. You will need to open this connection or if there is a convenient place to cut the pipe and later slip in a connector, we are trying to find the first source of restriction.

I have done both the draining and flushing to no avail...

Since there is no removeable connection on the inlet or outlet, it will need to be cut. Not sure I am the right person to solder a joint in, do I have options other than to call a plumber?

I really appreciate your help!

These days, you can purchase so called "Shark Bite" fittings that replace soldering. You cut your copper pipe and when finished with your repair, you simply insert each end of the pipe to this fitting. Done in few seconds. You can pressurize your water lines immediately. In my region, Shark Bite fittings are approved by Plumbing Code for residential installations. Home Depot now sells them in all basic sizes and configurations.

No more flux, solder, torch, Mapp gas, heat shield, acid brushes, steel wool... No need to call plumber. Shark Bite fittings are "LifeSavers" !

I agree with Milo, Harkbites are the home handuman's friend.