Since it's berry syrup, not particularly. However, the remaining air may lead to faster oxidation and loss of quality, similar to open kettle canning. I would put that jar at the front of the shelf and use it first. Next time you may just want to refrigerate that bit.

Carol

I agree that with acidic foods such as this too much headspace is less of a concern but it should, as Carol said, be avoided. Just put left-overs in the fridge. Don't process them.

And with low-acid foods headspace isn't something to play with.

Dave

Thanks guys.

Berry syrup never sits around for long in our house :).