It feels somehow significant that the Facebook reply ended up being its own message in a bottle.
I felt horrible for weeks that I had never responded, then I sent off a reply. I then promptly forgot that I did so, and abandoned LinkedIn for another year. I checked again last week for some reason and I had a year-old response to my response. I forgot to reply and only just now remembered this situation.
I'm now trying to decide if I should bother responding and risk another long delay, or pretend I'm dead.
then just explain that you don't use linkedin actively, and go from there. if they are not bothered by that they will reply. then possibly offer to switch to a different medium like email that you are less likely to miss.