Second, if the pager is outside its service area, it will not receive a page even if it is turned on. Third, if the pager is in a place where the radio signals sent to it are blocked, it will not receive the page. Pagers are basically small radio receivers, and as such, they are prone to the same limitations as small radios. Pages missed by the pager are not 'stored up', they are just missed, like a song on the radio. This will vary by time of day.
Most pages reach the pager in under two minutes.
During the busiest times of the day, some pages may take more than five minutes. During less busy times, it can be as little as a few seconds. I have a pager that only lasts two weeks on a set of batteries. Some features of the pager use more power than others. If you get a lot of pages, and the pager is set to vibrate, this can speed up battery use.