Why would the oil light stay on? - Cars & Trucks

That depends on the type of oil warning light being displayed. There are 2 types of warning lights

1. Low oil pressure light which all cars have
2. low oil level light which some cars have.

Low OIL PRESSURE warning means the oil pressure is below minimum and when this happens there will be insufficient lubrication of many engine parts because sufficient oil cannot get to all parts of the engine it is required to lubricate. Until the cause is identified and rectified the warning light will remain. If you run your engine with low oil pressure you will cause expensive damage to internal engine components.

Low OIL LEVEL warning means the oil in the sump has dropped to a dangerously low level (which may be due to an oil leak or abnormal oil consumption by the engine.) This warning means the oil level needs to be topped up and the warning will stay displayed until you top up the oil. Running the engine with low oil will cause expensive engine damage.
Since it is a 2 minute job, Oil levels should be checked fortnightly as a minimum, together with radiator coolant and power steering fluid levels, if you run the car most days each week as most people do.

It is possible for a warning light to remain displayed when the cause has been dealt with because there is a problem with the sender unit. However it needs to be established with alternative checks that the problem has been fixed before investigating if there is a problem with the warning light itself.