Just a quick question, can’t find an answer for.
When you spin at a Poke Stop you get your research task. That specific stop gives the same task to anyone who spins it.
How long before it gives a different task?
I have had people say it’s a different task every day, I’ve heard people say it resets weekly, I had someone tell me monthly.
Went to almost 30 stops last weekend trying to find that ‘use 5 razzberries’ task to get a Cubone with no luck. 
A day
00:00, Midnight, a new task will be available.
I thought it was daily, but, coworker who plays more, insisted was weekly. Which is annoying because he had the Razzberry task and said he got it this week (last week now) but couldn’t recall which stop, so I went to them all. Sigh.
Only had the Cubone task for 2 weeks now, but would be nice to be done with it sooner than later.
2 days in a row can happen, but it’s rare. It is daily. I’m a daily player, spun over 5000 stops.
If your local stop keeps giving the same tast for weeks, report it to Niantic.
Its definitely daily, and as @MrHeineken88 says the reset should be at 00:00. There are exceptions though. I didnt check in a while but a stop near my house used to reset later than that, whilst others did reset at 00:00. Im pretty sure this was cause it was a pretty new stop, just like new gyms have raid eggs at different times.
The task on each pokestop resets on 00:00 midnight local time, it’s rare to have same task on the same stop in two consecutive days
Have had a few times, that’s why I know it’s possible.