In the last 10-15 years, the jelly & jam jars began to say
"Refigerate after opening" on them. The risk is that like any kind of
preserve or fruit etc is that it can get moldy. Prior to this, a lot of
people kept their jams and jellies outside of the fridge and in all
likelyhood the jelly should be fine if only left out for a short period
but it's not a great idea IMO. Some things get moldy really fast such
as tomato sauce. Even in the fridge it gets moldy. I called Ragu once
and they said to only keep opened jars of sauce for 10 days which came
as a surprise to me.