Why can't ciliary muscles in the human eye relax like other muscles?
First of all, I should correct some points that were misunderstood. 
Don't change the question because this will lead to confusion.

"The way the lens becomes flat is by using spring-like connective tissue called choroids that pull it taught."

In classic ophthalmology you don't need to think about choroid in direct relation to accommodation: choroid is a sponge-like layer between the sclera and retina and in general it is consisted of blood vessels. The anterior part of the choroid continues anteriorly to became a ciliary body which in turn contains ciliary muscle - one circular muscle per eye. From the ciliary body/muscle spread zonules (zonule fibers) and they are fixed on the lens equator. 

Physiology: contraction of ciliary muscle causes zonules to became loosen and "free" the lens to became more convex and move the focus anteriorly (not choroid contracts itself). If the ciliary muscle relaxes then zonules are tighten up and the lens consequently becomes more flat (less convex) moving the focus posteriorly. In other words you can say it in the terms of depth of focus - convex lens gives less depth, less convex gives more depth of focus.

Thus, the classical choroid layer does not perform any action (look at your choroid related link - there are almost nothing about accommodation).

"Permanent state of contraction" can be physiological (=normal) as well as abnormal one, and it is very common in some conditions (muscles spasms). One example is priapism, where corporal smooth muscle contraction causes permanent and dangerous penile erection which can be medical emergency (priapism is by far more complex, so take the explanation like a metaphor). 

If we refer to "accommodation spasm" there is analogy to "muscle spasm" (and partially to priapism), but I should state we believe that spasm of ciliary muscle exists - since we don't see it directly. Probably (and take this sentence as speculation, since I cannot give you reference right now) the causes of this is not a muscle spasm itself, but the state of zonular fibers which cannot come back to their base state. I like the example with iron rod - if you will contract it fast and many times, at some point it can be "loosen" as well as fractured (and probably it does happens to zonules too). Probably (I say "probably" to underline the point we do not exactly know this), the "accommodation spasm" is partially misname and in future the investigations will clarify that.

Probably, you will learn some interesting facts from definition of "pseudoexfoliation" syndrome, but I do not explain it here because it is not related directly to the question. From wiki "has been known to cause a weakening of structures within the eye which help hold the eye's lens in place, called lens zonules"

Another example for analogy for continued "spasm" is the situation when one should care something heavy for a long distance without releasing the grasp - finally one can get not only spastic contraction but also severe ischemic damage to the fingers. 

Considering your case, you should know about pathological (degenerative) myopia where the eye expands posteriorly and consequently the focus is before the retina which should be corrected by minus lenses. It is well known fact that myopic eyes have longer axial length then normal eyes. Probably, it is your case.

So, as you can see, the answer to your question is not a clear cut, but assumption. The ciliary muscle does can relax, but probably the problem is more complex then only ciliary muscle related issue.

PS The image you reposted is a little bitconfusing one and is not exact. This one is classical and gives better understanding of the anatomy -