I always keep in mind that quote about the trumpet from a little organology (the study of music instruments) book I got years ago: "It is one of the most difficult instruments to play."
As adult learners, we make the terrible mistake of always being result oriented, instead of letting things happen. On top of that, we listen to good music played by the best artists in the world. The trumpet playing to which we expose ourselves comes from exceptionally gifted individuals who followed a long path of perfecting their art. It's good because it forms good taste, and bad because it skews expectations.
Kids (most of them, let's not consider the exceptional uber-gifted in this discussion) learn a different way: they're kinda pushed to pick up an instrument. They practice a little here and there, often no more than 1/2 hour a day for a couple of years. The development happens gradually, almost without them being aware. Even though there is the band director's expectations and pieces of increasing difficulty over the years, they don't monitor themselves in their way to a predetermined standard like adults tend to. Adults also tend to attach too much of their ego's self perception to accomplishements realized in activities they decide to undertake. All these are psychological obstacles.
There are some physical ones too. Sound production on the trumpet is a tremendous problem. For some, it comes easily, their embouchure is almost pre-formed. For the others, we have to do a lot of searching, because it's not exactly natural. I can very much relate to your difficulties. My own path has been, as an adult learner, much like what Dale has described for his beginnings. I had to come to the realization that my sound production (the combination of embouchure and everything else participating) was faulty and that I had to evolve my embouchure toward where the higher notes could happen. It's been very difficult, as this way of producing the sound did not feel as natural as the one that was a dead-end.
But the process is happening. My bad days a couple of years ago had me stuck at E 4th space (the note I could count on no matter what). Now bad days are more like A one ledger line above. A good day will see a clean attack on high C and reach high D or more. The variety of pieces I can play has greatly increased. There is no length of community band rehearsal that will find me out of notes on the 2nd trumpet parts. I've started trading parts with the 1st book players so they can get a break from time to time. I had compliments on my tone from other band members, including a former pro tuba player.
My biggest obstacle is being always tempted to go beyond my endurance limit on any given day, because I then have to pay for it for 2 to 3 days. I think that is another huge mistake we make as adult learners. The fine motricity and special type of muscle strength needed to play are no more developed in us than in kids who are at the same level of development. The very small and precise muscles of the face also do not give the same kind of feedback as the large ones we use when exercising. Fatigue is most readily detected through sound quality and the difficulty or impossibility of getting a note to come out, not by the sensation in the muscles. When fatigue happens, the worst thing to do is to try to force it. You may have done more harm than good by" trying everything" to make that G come out, making its absence a self reinforcing process.
Even though we are adults, we can't start by throwing ourselves into 60 or 90 min sessions every day and expect progress to happen. This in fact leads to a never ending plateau. I've had much better results by keeping my practice sessions shorter. Ideally, 3 times 20 minutes, with plenty of time in between, is best.
I'll add this to conlude: my progress has been associated with lessons taken from a very reputable teacher. He did not seem too interested in my range issues but the first thing he told me was that my sound was all but absent. Ever since, it's been the focus of my learning with him. The difference after a couple of years is huge. I know that most of what I have learned with him (which goes way beyond the sound production) is stuff that I could either have never understood, or that would have taken years of searching.
Last thing: check out Greg's mystery to mastery video series. It has some of the most useful stuff on sound production I have seen anywhere.