to be
to exist (humble)
Structure
- ある → ございます
This may seem kind of silly,
But does anyone know why ありがとうある is not a thing? Since ありがとうございます is the current usage.
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ありがたい is an い-adjective, therefore it would be ありがたくある if you wanted to use it with ある. Nobody does this because the whole point of the い form is that it’s not needed. And nobody uses あります for this either, because why would you deliberately make a set phrase less polite.
The う conjugation of い-adjectives is only used when the following word is ございます.
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Like @nekoyama said.
ありがとう is the adverbial form of adjective which modern form is ありがたい.
In the past the adverbial form shifted from く to う, but after some time it returned to く again, so most of the adjectives have く adverbial form like 早い->早く.
However, some adverbs that were used often didn’t return to く (this is often the case, that’s why many very often used words in numerous languages have strange conjugations). For this reason, we are using ありがとう in ありがとうございます phrase. Other examples are おはよう and おめでとう.
That applies to だ and です (you can say for example よくある問題 for example, lit. problem that frequently exists), だ cannot follow いadjective because it already has “to be” meaning, です is added for politeness. 
100% agreed, it became a set phrase (and it is best to remember it as such, and “ありがとう” as contraction of it), and there was no need to change it, no one uses ありがとうある or ありがとうあります.
(Though apparently older people in Hiroshima prefecture actually used ありがとうあります. It is uncommon now.)
By the way, some people also use ありがとうです which is ungrammatical (です should follow the adjective, so ありがたいです is correct, and it means something along “something is appreciated”.)
I hope it helps,
Cheers! 
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I noticed that with the example sentence “時間が [humble/polite] ので、ごゆっくり。”, you’re supposed to use “ございます”, which got me thinking.
I was taught that before “ので” you should use dictionary-form, but while it seems that “ござるので” is used, it’s a lot less common than “ございますので” 
I guess it’s a politeness thing, but as a general rule, is ます form preffered in humble speech where there’s a choice- would it sound weird to use the dictionary form here?
Likewise, should I be ignoring the dict-form ので rule for polite speech, or would ますので sound too stuffy if you’re just talking to a stranger who is not superior?
(Sorry if this is the wrong place to ask!)
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@RhinoINK
Hey 
When we have AexpressionB, then if an expression is が or けれども and you want to make it polite, then you should use polite forms in A and B.
If the expression is から、ので、けど and you want to make it polite, then you can (but don’t have to) use polite forms in A.
If you are for example working in a shop or talking to your superior then polite A is quite common. If you are just talking to a random stranger on a street then the short form is more common. From the point of view of politeness (and grammar) either you choose is fine.
With those expressions there is no need to worry about being too polite
I hope it helps,
Cheers!
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Hey! Thank you for taking the time to reply, that was really clear and helpful 
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Is “humble” actually the correct descriptor here? My understanding is that “humble” is usually used to refer to keigo verbs that indicate an action done by the in-group (e.g. you or your company) in order to downplay your own importance. Verbs like 参る (humble form of 行く、来る) or おる (humble form of いる). On the other hand, ございます is a neutral polite verb that is used without regards for whether the referent is related to the in-group or out-group (and usually is neither anyway because ございます, like its non-keigo counterpart ある refers to inanimate subjects).
(Japanese: The Spoken Language Part 1; as a note “distal-style” is how they refer to the use of です•ます)
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I came in here to see if this very question had been asked. Even the Tae Kim article linked under Readings says this:
It is neither honorific nor humble but it is a step above 「ある」 in politeness.
Okay, so I think I have an answer regarding this whole ござる situation (even if this answer might be a bit late lol). This will basically have to be small dive into humble language as a whole so here goes.
Basically, the ‘humble’ language 謙譲語 has two parts; one is for describing actions you do that in some way or another involve the person you are doing something to/for, and the other is for when you are only describing your own actions, but want to be extra polite in your speaking.
The first form, which is what most people probably think about when you say 謙譲語 is 謙譲語１, which includes the お～する pattern as well as some specific verbs. The second form, which can be called either 謙譲語２ (or 丁重語) only contains a handful of verbs.
The verbs which belong to 謙譲語２ are: 致す, 申す, 参る, おる, ござる, and 存じる.
Now, just as 尊敬語 can be used in plain form if you’re close to the person you’re talking to, e.g. 「今日、先生、いっらしゃる？」 this also applies to 謙譲語１, but not 謙譲語２. 謙譲語２ verbs are always used with 丁寧語, i.e. the ます form. So even though the aforementioned 謙譲語２ verbs have plain forms, those forms are basically never used and you will always see them as 致します, ございます, etc. This explains why you can’t have “ござるので” and it must always be written “ございますので.”
謙譲語２ is more or less just an upgraded version of 丁寧語 so a better description might be ‘extra polite language’ or something along those lines, instead of lumping together both 謙譲語１ and ２ into the same ‘humble language’ category. However, I feel it’s important to mention that you can only use 謙譲語２ when speaking about yourself and your own actions, and not other people and their actions, as that is the role of 尊敬語. (Which is also why I’m confused by the sentence 「タナカ様でございますか」in the “fun-fact” section which I found wasn’t explained all too well, but I digress.)
If anyone wants to get a better understanding of 敬語, there’s a playlist on YouTube which I highly recommend, and will leave the link to, that explains basically all you need to know about 敬語 in 5 parts: KEIGO/敬語. (The videos are in Japanese but there are full English subtitles!)
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