GPS are like your lover, you can’t just turn them on & off on demand.
It takes 12.5 minutes minimum to download the almanac which is valid for a number of months - this gives rough positions of the entire satellite constellation and enables a warm fix which is typically 20 seconds.
So the almanac allows the GPS to have a good idea of what to ‘look’ for. Once it has a connection to a satellite, it can then start picking up the ephemeris for that satellite which holds data for the coming 30 minutes. This takes 30 seconds for each satellite once the GPS is receiving the satellite’s signal.
So the ephemeris allows the GPS to know precisely what to expect if it’s powered down and then re-queried in the next 29 minutes, giving a hot fix which could be a second but at worst could be 20s. Turn on 31 minutes later, it reverts back the almanac.
If the time between GPS queries is longer than 30 minutes, it will need a warm fix (20 seconds) and then 30s to download the ephemeris if you want that to hand (which you don’t if you are not going to ask for a fix again in the next 30 minutes).
GPS queries more frequently than 30 minutes will need to be on for 30+ seconds towards the end of your 30 minute sliding window so it can pick up the ephemeris. You can do what you like in the first 29 minutes, but if you want to be sure of a hot fix on minute 31, it will need time to download. Obviously this data is coming down all the time so it may have accumulated enough, but it’s very hard to tell without all sorts of arcane AT commands. Or just testing, try running the GPS for five seconds after you’ve got your hot fix and see how that fairs. The different chipsets as well as the antenna’s will all have different levels of success.
TL;DR: You can’t just turn on a GPS and get a good fix without letting it collect the data it needs.