Is ゆっくり the only mimetic expression that accepts the honorific prefix ご?
And for that matter, why does it take the honorific prefix ご- which is usually meant for 漢語?
There are a number of exceptions regarding the usage of お/ご, and, ultimately, you have to learn them individually.
According to a survey by Tanaka (1972) based on the word usage of newspapers, お attaches to a kango roughly 20% of the time, but ご very rarely attaches to a wago (they identified only ごもっとも and ごゆっくり). Even a long academic article dedicated for this topic lists only ごもっとも, ごゆっくり and ごゆるり. ゆるり is mimetic, so ごゆっくり is not the only mimetic expression that accepts ご. Still, you can say the number of such words is very small.
Kango that take お tend to be common and daily words such as お風呂, お料理, お財布, お写真 and お掃除. A few words accept both お and ご, and in such cases ご sounds stiffer (e.g. お誕生 vs ご誕生, お返事 vs ご返事). FWIW, I feel ごゆっくり, ごもっとも and ごゆるり also have formal, polite or even a little pompous overtones.
For clarity, I edited my answer by adding the text inside [] in the 1st paragraph below:
In addition, if one prefers to use a one-words sentence like "Relax!", saying only "ゆっくり” sounds confusing [because saying only ゆっくり would mean "be careful, do it slowly!", instead of "relax!"]. Maybe ゆっくりどうぞ could work without a ご but, at least I wouldn't say so.
So, ご it is partly to ensure that the person to which ゆっくり is adressed to feels that he/she hears it in a positive way.
p.s. On the other hand using both ご and どうぞ in a sarcastic way, the meaning could also be "You are just sitting there on the sofa and you really should realize yourself that while I am washing the dishes, there are lots of things that you could do, like maybe taking out the rubbish!"
まれに、和語であっても、「ご」が付くものがある。「ごもっとも・ごゆっくり・ごゆるり」
って書いてありますね。 sakura-paris.org/dict/…