Our veryold toilet does same thing. I've been told that lime buildup on the inside of the bowl and trap can make it rough surfaced and thus slow the flow.
For now we just deal with it, using chemicals when absolutely necessary to unblock it but usually just a rubber helper does the trick. If you have water leaking down from the tank even after it's refilled, you may have a leaky flapper valve. These are easy to replace including the seat with a single unit that has a sticky clay like epoxy that just shoves over the old seat. You then attach the new flapper's chain to the flush handle, adjust for desired flow and you're done. Tom Fowle