When last we used them, they were typically only good on the day they were issued. (about 3 years ago)
While there is typically no limit on numbers, there are some important limits on obtaining them and practical limits on using them. We usually only held one at a time, except BTMRR + Splash.
The thing is, it takes time to walk between attractions. Odds are also about 50/50 they won't be much benefit late in the day.
We have stacks of paper FP we never used, because we either never returned to use them, or standby lines were under 15min and the FP queue was closed/FP was no benefit. Even when we did use the swap passes, after dark the passes were often of negligible benefit.
Now as for the limits. In order you get a RS pass, the under-height child has to be present. RS is only available at rides with height limits, and toddlers have a very finite tolerance for waiting around.
Some folks have reported a strategy where one parent rides in the am , then leaves with infant for nap, then 2nd parent uses swap passes. that didn't work for us.
Since this is summer, I should add: 2pm to about 5pm summer weather is typically real-feel over 100 degrees, while sometime between 3pm to 7pm is often thunderstorm hour. The best strategy we've found is to get indoors during the worst of it, especially when a young child is in your party!
All of the above is why we found RS were most useful if we used them right away.