Hi disco-very, just signed up to this site as i was having a very very similar problem to you albeit on a rpi2. Just wondering, are you using the built in wifi adapter?
My problem was solved when i swapped out my wifi dongle and replaced it with one of those wee edimax dongles ... what i was using was a Realtek Semiconductor Corp. RTL8191SU, - so my thoughts, in my particular case are:
1) perhaps i need to install newer drivers
2) perhaps it was drawing too much power
Now i am more inclined to 2) in my particular case as 99% of my pi problems are power related, but i presume that the hifiberry amp comes with adequate power. So looking at 1), is everyone else using the onboard rpi3 wifi with no problems?
perhaps, if you have access to a wifi dongle it might be worth a go?
t.