Don't have a Toro, but typically the mower deck is run by a solenoid clutch - no power, no blade rotation. Easiest scenario - a loose push-on connection.
Trickier - I've run into this with other coils, specifically automotive ignition -
These coils have very small gauge solid conductor wire so they can get lots of turns in a small area - this gives more "pull" for a solenoid. Occasionally, due to vibration usually, this tiny wire will get a hairline break INSIDE the coil somewhere.
As the coil cools, it contracts and this break makes contact (the wires touch) - when you apply power, the coil warms up and the break separates again - no current = no blade rotation. Cools off - ends of the break come back together, blade runs.
Very frustrating the first time it happens to you - "fool me once, yada yada..."
If you're lucky, it'll just be a loose push-on - fix may be as simple as slightly squeezing the female half back together so it makes better contact, or crimping on a new one (try auto parts stores, these are usually 1/4 inch size)
Hope this helps... Steve
If yours takes long enough to start working again and you have a multimeter, as soon as it stops working you may be able to pull off one of the connectors to the solenoid and quickly check continuity of the coil - this should tell you whether you need a new solenoid or there is a wire loose/broken somewhere else in the circuit.
