This comment below How long will last the Blue Origin New Shepard space flight? says (in part):
The words "suborbital spaceflight" as the first words on Blue Origin's webpage for the New Shepard mean that, yes, the flights will last a few minutes.
Question: How many hours long is Earth's longest possible sub-orbital flight?
How many hours long is Earth's longest possible sub-orbital flight?
"Orbit", and thus "orbital" and "sub-orbital" is another one of those words like "rocket" whose definition alters significantly with context. Any trajectory under gravitational influence and not dominated by atmospheric influence can be considered an "orbit", but here at S.SX we usually take "sub-orbital" to mean "a trajectory which does not permit a complete orbit because of unavoidable aerobraking and/or lithobraking effects".
The longest possible coasting-only sub-orbital flight from Earth, then, is an elliptical orbit which goes almost to the edge of Earth's gravitational sphere of influence (itself an extremely fuzzy and context-dependent concept) at apogee and returns to Earth with a perigee low enough to guarantee prompt reentry.
Wikipedia tells me Earth's Hill Sphere goes out to around 1.5 million km; my training and experience in Kerbal Space Program + Realism Overhaul tells me that any Earth-bound orbit going to, say, 45km altitude will reenter promptly.
This orbital calculator informs me that the period of this orbit is 75.3 days. Since we're going at 11 km/s at perigee, we can more or less ignore the time spent on the atmospheric end of it; the period of the complete orbit is almost exactly the same as the period of the suborbital portion of the trajectory. Since we're going out pretty close to the edge of the Hill Sphere and we'll be moseying along at only 50 m/s at apogee, perturbations from other planets might shift this period by a little bit.
If we use the "two-fifths power" definition of sphere of influence (I don't know if this has a better name?) the apogee needs to be closer, around 0.92 Mkm, for a period of 36.3 days.
There is, almost assuredly, some gonzo trajectory which relies on perturbations from Jupiter and Saturn to juggle the spacecraft at the very edge of Earth escape before sending it home a year later, but I'm restricting my solution to the tools available to a poor unfrozen caveman rocket scientist.
At least 23,000 km. The Sänger anitpodal bomber concept:
sled launched, boosted to suborbital velocity, 'skips' off upper atmosphere
Eugen Saenger conceived of a winged spaceplane while a doctoral candidate at the Vienna Polytechnic Institute. His 1933 Silverbird concept was for a Mach 10 glider that would cruise at 160 km altitude. ...
It would have a hypersonic L/D ratio of 5.1, reach a top speed of Mach 13 at burnout of its rocket motor, and then enter a 5,000 km long glide, reaching a stable Mach 3.3 cruise at 50 km altitude.
The final refinement to the design was his 1944 report Concerning Rocket Propulsion for Long-Range Bombers, which featured a spaceplane 28 m long with a 15 m wingspan and 100 tone take-off mass. The glider would reach a top speed of 21,800 kph and have a range of 23,400 km.
According to Wikipedia's list of Flight Endurance Records, the longest continuous flight of an airplane thus far has been 623:57:00, recorded July 11 – August 8, 2018, flown by an unmanned Airbus Zephyr 8 drone.
It was a flight, and it did not achieve orbit, thus a suborbital flight.
This is of course not the theoretical maximum, it is the publicly known practical maximum that has been achieved so far as of the writing of this answer.
