That may be true but what can happen is when the Beacon is in an area where it is constantly trying to update and find a good GPS signal it drains the battery much quicker...same as when a phone is in a poor reception area and uses more battery life to acquire a signal. Some of the remote areas tend to have the Beacon searching for a GPS signal lock and it drains the battery faster than the flight time of the drone battery.
You describing a situation that doesn't exist. The beacon doesn't update by searching, when the app is first opened up it checks for updates. If there's a new update it downloads it. Not until the next time you connect ether the drone or the beacon to the app will the update get pushed from the phone to the beacon and it's likely you'll be forced to also update the drone before it will let you fly. You really don't want to find out there's an update when you're out somewhere and turn it on. There's only been 4 or 5 since the drone came out over a year ago so it's very unlikely. More importantly the drone will use a 5 min of so of it's battery if there's an update. Better to turn it on at home, if there's an update it gets done then, not when you're not out somewhere getting ready to fly, when that happens you'll waste allot more then the beacon's battery.
It's only acquiring a GPS signal for a min or so right after it connects to the drone. If you turn on the app it acquires acceptable GPS signal far quicker. If the signal gets weak the drone will tell you and stop flying. Keeping the beacon turned on will not help with acquisition, every time you connect the beacon with the drone it's going to start over acquiring signals. It's not like keeping it turned on gets you anything. Your description of what a phone does when confronted with signal loss isn't correct, a receiver is far more sensitive then the transmitter, when the phone comes in range of a signal the phone attempts to communicate with the tower. Since the receiver picks up the tower before the phone can actually communicate with it, the phone is designed to increases it's transmitter strength to speed up that link. That's what wears down the phone's battery when signals are poor, its transmitter, not it's receiver. The GPS doesn't work that way, it's a receiver only, when a GPS signal strength is low aka high signal to noise ratio. It can't turn up it's receiver, it can try and improve the signal with an algorithm if it's smart enough GPS but that's a few cpu cycles, not like cranking up the power in a phone's transmitter to establish a link. GPSs are used globally with relatively small batteries because they do not require much power.
I know 2 other guys flying SD2s and all will go multiple flights with a single beacon charge, For all of us it's a once a day thing, in their case 3 flights or drone batteries, in mine five 20 min flights and there's some battery to spare. My beacon is over a year old with well over 75 flights so it's is far from new, every flight it get's connected to the drone and the app so there's 2 WiFi connections, not sure how much extra that uses but it's more traffic then the drone alone. As far as I know you're the first person I've seen mention the beacon's battery as a limiting issue and the drone has been out over a year. If the problem you describe is happening, you may want to talk to them about it before it gets too old, it sounds like your beacon may have a weak battery.