I don't know if this is related but I have a gmail account I seem to only occasionally get updates for. That is to say it seems there's a delay between gmail's

I don't know if this is related but I have a gmail account I seem to only occasionally get updates for. That is to say it seems there's a delay between gmail's servers receiving an email and that email being sent to my client, usually days up to a couple weeks and updates happen all at once; just the other day I had 18 emails come in at one time rather than trickling in over a week or two. In this case, it's an old account which doesn't see any outbound email traffic (I do still get inbound messages which I actually want, newsletters and such); I wonder if account activity has an effect on the urgency with which said account's notifications are delivered. The problem otherwise sounds similar except with alerts instead of mail. They also sound dissimilar because you seem to be missing things which you know you shouldn't, even after receiving updates (and it's alerts instead of mail). I would only really consider them as possibly related because of the G commonality. Just some anecdata in case it's helpful.