This is an enormously frustrating issue. I interpreted the question more personally, as in how I deal with it as an integrator, ie: how long should a camera be down before it is fixed. Most VMS's will notify of a lost video signal fairly quickly. Typically (again, depending on the customer) they will do some minimal digging into the situation to inspect for anything obvious and then call us.
Then, as Ethan stated, it varies substantially on the customer/environment and maintenance agreement in place. The race to zero has changed our service/maintenance offerings/response over the last 15 or so years. We used to sell a service agreement with every system of any size. Now we hardly sell any. Further, we service a more rural, spread out territory of small to mid size customers. This makes it harder to give red carpet service, especially for budget conscious customers who don't have service agreements. "Oh, the 8 camera system we put in at your mini-storage, 60 miles away, 2 years ago, for $2,500.00 has a camera out? We'll try to work it in on our next trip down that way." "Oh, and yes the camera may still be under warranty, but we'll have to charge a labor charge to swap it out."
This can then easily lead to TWO service calls and a pesky RMA process with the manufacturer, possibly taking 2 weeks, (if you're lucky), UPS charges, etc. And, the invoice for the work if billed honestly for time and expense involved: 4 hours travel, 2 hours on site, 240 miles driven, etc. should be around $500+ and that's likely not going to fly, especially for a camera under warranty.