How long can you leave a synthetic sleeping bag in compressed its stuff sack before you lose insulation? 2 days? 2 weeks? 2 months? The manufacturers say "long periods", but don't define it.
You shouldn't leave your sleeping bag compressed any longer than you need to. Store it out of it's bag on a shelf, hanging up, or in a large breathable storage bag. Only stuff it into it's stuff sack or a compression bag when you're packing it. If you store it compressed it will lose loft, which is what gives you insulation. How quickly it loses loft varies depending on the type of synthetic insulation, and how compressed it is.
Assuming you're going to be sleeping in it every night, the longest it would be compressed is 16hrs at a time so you don't need to worry about it. If you're traveling then it may stay packed for a couple of days, in which case only compress it as much as is necessary, and unpack it as soon as you've stopped moving for the day. Never leave you bag compressed longer than you need to.
Sleeping bags will lose insulation over time no matter what due to regular wear and tear, but you can minimize the wear and tear by properly carrying for you bag, some bags can last a lifetime with minimal insulation loss if cared for properly.