Electrical – Outlet lost power

Not an uncommon problem. I have had a lot of problems with GFI's the last few years myself. There are a few likely causes:

1. A fault still exists and will not allow the GFI to reset.
2. The GFI tripped due to an overload and the differential circuit was damaged, thus the outlet is now toast. This seems to be a common complaint with standard 15 amp GFIC's. they don't take current spikes well. In your case 1500 watts on 120VAC is pulling around 12.5 amps, which is getting close to max capacity. Sometimes the initial current draw is much higher as the resistive load needs to heat up a bit before it reaches its operating impedance. A "cold" load can offer a much lower impedence and cause a short duration, but large spike of current to flow at turn on. Very common on motor loads, but not uncommon with filament heating or lighting.
3. Sometimes if you turn off the power to this GFI at the breaker, then push the test and reset buttons, then turn the power back on again, the GFI will default to the tripped condition, but will reset.
4. Disconnect any wires connected to the "Load" side of the GFI. Unplug all loads from the GFI itself, and give it a try.
5. If none of the above items work for you, you will probably need to replace the GFI. Find one with a 20 amp rating instead of 15 amps, assuming that 15 amp is what you have now.

First off. The only way to provide proper "grounding", is to install a grounding conductor from the panel to each outlet. Providing AFCI and GFCI protection to the circuits is helpful, but these devices will not provide "grounding".

If you switch from 2-prong receptacles to 3-prong on these circuits, you should not connect anything to the grounding screw of the receptacles. You should also (technically) install labels at each outlet that read "GFCI protection" and "No Equipment Ground". Though, these labels aren't common in residential situations.

1. Replace GFCI breakers with CAFCI breakers and add GFCI receptacles to the first-outlet on each circuit.

This is probably going to be your best bet. In this scenario, the CAFCI breaker provides protection to the entire circuit. The GFCI protection being at the first outlet, means that while the wiring from the panel to this location is not protected, the rest of the circuit is protected.

2. Keep GFCI breakers and add AFCI receptacles to the first-outlet on each circuit.

This isn't a terrible option, although the AFCI device will not be protecting the wiring between the panel and the device. Also note that an AFCI device only detects line to ground arcs (parallel arcs), while a CAFCI device detects both line to ground and line to line arcs (parallel and series arcs).

3. Replace GFCI breakers with Dual Function AFCI/GFCI breakers.

If you could actually find these (and could afford them), this would probably be your best course of action. Unfortunately, these devices probably don't exists (yet) from most manufacturers.