It is strange that the whole family is missing.

As you say, they could have been at sea.

Possibly the last name has been wrongly recorded.
My original index was compiled from the IoM FHS transcription which was such a mess that it was redone using LDS microfilms. This was done once more using microfiche supplied by London.
All this is to say I am confident they are not in the IoM portion of the 1851 census under Ash(e) or any other name.

Lastly, they could have been omitted either because no schedle was delivered or the schedule was omitted by the enumerator.
The first involves two visits to a residence being omitted which seems unklikely. The second involves a gap in the enumeration and as the schedules were numbered this also seems unlikely. I have not come across any unaccounted schedule numbers.

A mystery.