We have gone through a similar situation over the last 6 months other than it was a hospitalisation followed with a very short stay in a nursing home followed by my MIL’s death before Christmas just gone.
As long as he is in a care/nursing home that you/he is funding you can still use the car as suggested as he will still be eligible to claim his DLA benefit and as long as that is still being paid still retain the car.
Should he need to stay in an NHS hospital for up to a continuous 28 days again this is OK. However once over 28 days you need to tell DWP/Motability and his DLA will stop until he is discharged from hospital.
If he was then still in hospital for a further unknown period you would have to give the car up although motability will normally work with you if the hospital stay was shorter than a further 2-3 months.