With a home this old it probably has been updated.
Are there still 2 prong outlets? If modern 3 prong some level of updating has been done. It is possible that they used back stab outlets very easy to wire but not reliable.
With the circuit breaker off, pull the outlets that are not working. Use caution when pulling the outlets because the original braided wire may still be there and the insulation can be fragile. Examine the connection to the outlet--if the wire is pushed into a hole, this is probably your problem. Most outlets have a slot next to the hole that will release the wire or it may have burned loose. If there are screws on the side move the wires to the screws or purchase new outlets with screws.
If you find plastic-coated wires, this is good news, as all the wiring was replaced. I have replaced hundreds of these back-stabbed outlets and this is where I would look. I've found everything from a wire totally burned off to ones that just slide out of the outlet.
There is also a slim possibility of a wire nut being loose but that is really rare. Replacement only takes a few minutes and is something most DIY folks can do with just a screwdriver and pair of wire strippers.