Aspect following должен

Question

Is there any rule governing the choice of aspect following forms of должен? It seems that in a negative sentence with должен, the best choice is often the imperfective, i.e.:

Мы не должны были терять очки.

Even with regards to this, though, I am not sure, since Google shows almost as many results using the perfective as the imperfective in sentences such as "Mы [не] должни были выигрывать/выиграть." (The imperfective is still more common.) So:

1. Which aspect is generally correct in a positive sentence with должен? Can one use both? (If so, is there truly a difference in meaning?)

2. Which aspect is generally correct in a negative sentence with должен? ("")

3. Which aspect is generally correct in a question with должен? What about a negative question, i.e. [ ]?

Не должны ли мы стремиться к такому идеалу народной жизни...

Answer 1

The fact is that должен in no way influences the choice of aspect.

1. Both "Мы должны выигрывать" and "Мы должны выиграть". The former implies a regular pattern - we must always win; the latter - we must win once.
2. не has no influence here either
3. see #1

To quote a popular site for Russian learners,

"The aspects are:

Imperfective - Incomplete, ongoing, habitual, reversed or repeated actions

Perfective - Actions completed successfully."

That's a very rough explanation, but it's important to keep this whole должен business out of it.

Answer 2

Depending on the meaning you want.

If you say

Мы не должны терять очки.

It means you should not repeatedly lose your eyeglasses.