We had this effect one of our gaming websites, but in reverse: we accidentally added around 900ms to every page load. Gameplays dropped by around 15%. We removed what was causing this and they instantly went back up.

People played it mostly during breaks: lunch breaks (our peak load was during lunch hours in the US), "smoke breaks", etc. So they didn't have a goal, they just had time to spend doing something. Each gameplay took anywhere from 1-5 minutes. Users averaged to 5 plays per day. Our guess was the extra load time caused people to hit some exactly poor threshhold where they were able to play 1 less game during their time allotment.

Edit: we were curious and A/B tested it and saw the effect too. We didn't run it for too long, but a 15% difference is quick to verify when you're measuring something that happens 35 million times per day.