When using もう and まだ in a negative sense, does the negative verb always have to be in the present continuous form i.e. 来ていません、食べていません etc? If so why is that?
Example sentences:
いいえ、まだ買っていません。- Correct
いいえ、まだ買いません。- Incorrect
My translation: No, I haven’t bought (it) yet.
(This was written before @Choko posted her comment but the two seem to agree.)
The easiest answer to your question is no, it is not that simple. It depends on the nature of the verb and what you want to say.
Your reference to "present continuous" suggests that your are not familiar with concepts such as "stative", "durative", "punctual", "subject change" and "continuous change" verb groups or the resultative state in Japanese.
This is quite a big subject to explain (there are probably several theories) but it is the key to the solution you are looking for: I found this paper, from @snailboat, quite useful.
BRIEF EXPLANATION OF UNDERLYING GRAMMAR & USE OF ADVERBS
There are not really any short cuts to studying something like this but, in relation to your question, I would summarise this as follows:
Verbs like 来る can be classified as "subject change". In its plain form 来る describes an unexecuted and (probably) future action. In its ている form, 来ている, it usually describes an action that has been executed and the result is still being felt (eg the subject has come and is still here). This is also referred to as in the resultative state. These verbs are different from verbs such as 騒ぐ which in its ている form describes the continuous action (or state) state of making noise rather than a "resultative state".
As you know, adverbs such as まだ and もう are used to describe or refine the action. This can be can be quite important. For example, in the case of
まだ来ていない
来ていない, as the negative form of 来ている, describes the (opposite) state that has not happened. The subject has not come (and is therefore not here). The adverb まだ reinforces this meaning and might be used to imply that somebody was waiting for it to happen or it was over due.
However, getting back to your question, the adverbs もう and まだ can also be used with such plain form verbs in the negative form but their appropriateness also depends what you want to say. For example:
彼はもう行かない。= He is not going again. (ie in the future)
Further, although the ている form of subject change verbs are usually used to describe a resultant state this is not always the case. One way to describe a continuous state using a subject change verb is by choosing an appropriate adverb. A good example is the verb 死ぬ, to die. The following sentences should illustrate this:
僕の猫は死ぬ = My cat is going to die.
僕の猫は死んだ = My cat died.(see note 1)
僕の猫は死んでいる = My cat is dead.
僕の猫はだんだん死んでいる = My cat is slowly dying.
By adding the adverb だんだん the predicate 死んでいる has changed from resultant state to continuous state.
So perhaps the answer to your question is:
No. It depends on the nature of the verb and what you want to say. If the combination of an adverb and a verb does not feel right the best course of action is to consider what you want to say and whether the sentence you have made really means what you want it to mean. This is illustrated by the other example you give:
いいえ、まだ買っていません。 (A)
いいえ、まだ買いません。 (B)
(A) is correct if you want to say: No I have not bought it yet. (B) might be correct if for some reason you wanted to say "No, I am still not going to buy it." (note 2)
Note:
If we accept the saying a cat has nine lives then perhaps we can say it has to die nine times before we can say it is "permanently dead", as in it leaves this world for the next. If we can say this then perhaps before it loses its ninth life we can also say:
僕の猫は死んだことが8度ある：My has cat died eight times.
...and it would not be correct to use 死んでいる because the cat is still enjoying its final life.
According to this paper (thank you @snailboat) and my own intuitions, the core difference between the two is precondition fulfilment: -ていない is used simply for the lack of an action (or its completion), while -ない is used for the lack of of a precondition being fulfilled for that action to occur.
(The paper talks about it in terms of intentions, but it seems to me that もう/まだしない verbs can take impersonal subjects as well. Correct me if I'm wrong.)
With まだ, this works out like this:
まだしていない is 'the action isn't completed yet' (i.e. it can happen/finish whenever and we're just waiting)
まだしない is 'the conditions for the action beginning aren't fulfilled yet' (i.e. there's something still lacking before it can begin, and just waiting isn't going to get us anything if we don't complete the prerequisites)
With もう, it works out like this:
もうしていない is 'the action is no longer occurring' (for whatever reason)
もうしない is 'the action will no longer occur' because a precondition is no longer fulfilled - especially if that precondition is someone's intention (e.g. '[I've decided that] I won't do it anymore').
With もう at least, the difference is perhaps better stated in terms of current versus future situations. もうしないと決めた is quite fine, since your decision affects what'll happen in the future, but *もうしてないと決めた is very strange - since もうしてない is a statement about what's already the case, your decision should have no bearing on the situation. Similarly, you can say もうしない for 'I won't do it anymore' even if you're still doing it at the moment, but if you were still doing it and said もうしていない, you'd be lying.
As far as I know, まだ～していない is the norm and まだ～しない is also possible for many non-durative intransitive verbs, such as まだ来ない, 届かない, 終わらない, etc.
There may be some subtle differences, e.g. していない may suggest the existence of some kind of evidence and therefore be more objective, and しない may be more subjective. Apart form them, I think the two expressions are generally interchangeable.
If the verb is durative, like 買う, まだ～しない is rarely used and often means not going to ... yet (するつもりはない) rather than have not ... yet.
いまだ～せず was used in classical Japanese, and still can be seen in news titles or something.
Will it make more sense to you if ている means have (いる/ある) + done (て/た)? Similarly, もう来ています and もう買っています can mean have already come/bought, too. ている is an ambiguous and relatively recent invention. So you may still find something like まだ食べません/買いません in old books.
However, “why” is never an easy question to answer. Although ている can mean “have done” in both positive (すでにしている) and negative (まだしていない) sentences, した is just more common than している.
As a side note, the した/している/しない/していない (but not しなかった or していなかった) contrast seems extremely complicated to me when it comes to the present tense or untensed expressions.
