I have a web application that displays the status of batch processing jobs on our computer cluster. To me, the title should read:
but I really don't know why and I'm not sure I'm right. Could you kindly explain?
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In the phrase, job is an attributive noun: a noun functioning as an adjective qualifying status.
In English, adjectives are not inflected for number. In the phrase red apples, the adjective red doesn't alter depending on the number of apples; neither does it alter if the apples are different shades of red (so there is more than one red).
Thus: Job status. There may be different statuses, and different jobs, but job here doesn't get inflected: it's acting as an adjective.
There are those who support the demise of the possessive apostrophe; who maintain it's acceptable to talk of childrens clothes, mens wear instead of children's clothes and men's wear (as opposed to the compound nouns childrenswear, menswear, which can't have an apostophe in the middle). On this basis, Jobs status might be acceptable for Jobs' status: using the apostrophe is fussy and could even lead to confusion with the late Steve Jobs.
However, having two s together in the middle of the phrase looks odd and it's not easy to say distinctly. There's not much difference between saying jobs status and job status. Purely on practical grounds in this case, it's another character in a column heading.
Given that using an apostrophe seems overly fussy, omitting it is still currently disputed, and the singular job is understandable and justifiable, use Job status.