Check if the thermostat is set to auto and not fan. The auto setting will turn off the blower when the condenser shuts off. It may run a few additional minutes at the end of a cooling cycle.

auto/ the whole unit works proper at night, then acts up later in the day

Sounds like the outdoor condenser is tripping some safety switch which turns it off but not the indoor blower. The indoor blower keeps blowing because the thermostat is telling it that it hasn't reached the setpoint temperature.

That sounds like a good theory. The condenser may be shutting down due to high temperature during the day. A night the sun goes down and the temperature drops. The cause may be due to the run capacitor is no longer within the proper range and causing more current to flow. This extra current is causing the motor winding to be overheated. You should have an HVAC company investigate this before you cause damage and create a larger repair bill.