James Holland said:
as weapons improve armour improves as armour improves weapons improve. and so soon those AP bullets would be of little to no effect.
It's not as black and white as that. There is a limit to how far you can take any particular type of armor or weapon before you hit a "softcap", the point where further improvement becomes overly expensive, complicated, logistically unmanageable, or something similar. Developing new types of armor or weapons to defeat the other takes time and resources and there's no guarantee that these new developments will be available when needed. If you haven't yet developed a clear-cut counter to the other then its entirely possible you're stuck in a deadlock of sorts, and factors other than pure performance, like cost or ease of use or maintenance, begin to dominate.
The best advice I can give when it comes to thinking about military weapons and armor (or any piece of equipment) is not to imagine them as standalone components, but as a single piece to a larger whole. A new type of rifle and/or ammunition may be able to penetrate more armor and at longer distances, but it may also be heavier, more expensive, more prone to misfires/failures, or any number of other things that would reduce its actual effectiveness. Perhaps its more difficult to use by soldiers, or it may just have a number of different traits which are simply a bad combination. In contrast, a weapon considered to be under-powered may be cheap, easy to use, or very reliable, drastically increasing its actual effectiveness relative to a supposed replacement (or rather it is the replacement that is not nearly as effective as its "performance characteristics" would imply).
A good example is the M4 Sherman tank of World War 2. It was initially (based on my limited reading) more than a match for German light and medium tanks in the North African theater. This changed by D-Day in 1944, where they were vastly outmatched by newer German tanks in terms of "performance". They were under armored, under gunned, and prone to fuel explosions when hit, unlike their German counterparts. They were also very cheap, reliable, and their widespread use meant that transportation on roads, rails, and ships was greatly simplified compared to what would have been required had several new tanks been developed and produced in large numbers during the war.
In addition, remember that weapons and armor do not operate in a vacuum. And I don't mean the physical kind of vacuum that boils the water off your tongue at the same time that it freezes. I mean that weapons and armor don't operate alone, but in concert with elements from many other weapons and equipment all at the same time. Part of the reason the U.S. was able to get away with using the M4 tank later in the war was because it had other weapons to take enemy tanks out with, such as tank destroyers, aircraft, and even some infantry weapons. Not to mention numbers, strategic bombing, and inept leadership at the top levels of German military command. The M4 was "good enough" to get by with given the state of the war at the time.
Everything is interconnected somehow. Remember that.