I think I know what going on, and it's not a bug, it's a bad assumption that we all make as explorers. We all say, we always plot a route on a full tank, but that's actually almost impossible, I will explain what I mean and why it affects you in that way but not me.
When I reach the end of my route (or log out and back in same thing), I plot a new route, but while it looks like the fuel tank is full it never is. You see we emerge, fuel scoop, move out of fuel scoop range of the star and plot a route. But the moment we exit fuel scoop range we are using fuel, the fuel tank is no longer full, it's only fractionally under full, but by the time we plot the route it's not full, so it will plot a route that's based on fractionally less fuel, and a higher jump range, than a full tank.
Your screenshot above is the clue, you are in a very dense area of stars, sometimes the distance between stars is well under a single ly, whereas I am out further where the stars are at least several ly's apart, so the tiny fraction of fuel difference between plotting and actually scooping full and jumping right away makes no difference, so I never experience it. So if you jump in, honk, find a single star system, immediately line up and press jump to the next star then the amount of fuel you are carrying is very slightly more than when you plotted the route. So it doesn't affect 99% if players, but if the stars are dense enough there's a tiny chance that one of your jumps will be out of range because you have slightly more fuel than you had when you set up the route. That's why it sometimes fails after a few jumps.
The same when we log back in, we have slightly less than a full fuel by that time because no-one logs out in the fuel scoop range of the star, so we have that tiny fraction of fuel less than full, and it plots distances based on that. The exact precision of amount fuel of scooped and the amount we have is to small to pass on to players, I am not sure how many decimal places they calculate it to but I think it's 4, but it's generally more places than we players have given to us, so it looks like, say 32 tons of fuel, and everything tells us it's 32 tons, but it may actually be 31.8824 tons, and that is enough, when stars are really close together, to make that difference, because distances and positioning are also calculated to 4 decimal places.
So that should explain why sometimes you get an out of range warning after a few jumps. Still not sure about the first jump being out of range after logging back in but I am sure there's something there that should explain it, but my heads already sore after all that thinking......
So in theory it should only happen where the starts are densely packed and stop when you leave that area.