their or your

Yes. "Your" would be correct if preceded by "those of you who...".

The statement is being made to each person affected. It’s trying to be personal, so the company uses “your.”

It's still wrong though, Blatham has already given the correct answer.

All you're doing is muddying the waters and making things more confusing. If you don't have anything to add, and in this case you don't, you should just keep quiet because you're doing more harm than good.

It is grammatically correct.

In English, 'your' can either be second person singular or second person plural. In this case it is being used as a plural pronoun. It simply means that the pronoun "those" includes the reader.

You could slightly clarify the sentence by specifying the pronoun "those" as in...

"We are truly sorry to have disappointed those of you who have showed your support from early morning,"

The "of you" is not needed. It is implied in the first example.

Also, the conjugation of "show" should be "shown."

To be truly personal, and grammatical, the sentence could be written as, "“We are truly sorry to have disappointed you who have shown your support from early morning,” since "you" is also used to indicate second person plural.

Blatham is right. Without "those of you," the word should be their.

The statement was made by a speaker whose native tongue is Chinese. Have you ever read instructions for devices made in China?
That being said there is no legal authority for grammar, there are common conventions, that are used by most people that earn a living writing. Matters it not, how said it is, as long as understand it you do. Yado son of Yoda.

It is grammatically correct? According to what authority? Oh wait that's right there is no authority for grammar spelling or pronunciation. These are all conventions, used by english teachers so they all teach the same rules.
Dictionary publishers do in depth studies of how the language they are writing a dictionary for is currently used. They give precedence to publishers, and writing professionals.
Dictionaries don't decide definitions, part of speech, or spelling. All they do is compile the most common usage of these factors. The single purpose of language is to communicate. The rest is analogous arguing over the proper way to drink tea. Pinky extended, or no.

It is grammatical. The authority is simple agreement of person. Otherwise, it would be ungrammatical. In regard to "correctness," that's your hang up. Deal with it.