After introducing an acronym, how faithfully must I stick to its use?

For a scientific paper, most publications dictate that you write the term in full the first time you use it, followed by the the abbreviated form in parenthesis.

• ...that can be easily diagnosed by Magnetic Ressonance Imaging (MRI)

All other times you are expected to use the acronym without parenthesis. If it's a long paper, and there are chapters, you are expected to write it in full the first time it is mentioned in each chapter. As for using several acronyms, say 4 or 5 in a short sentence, I would use some creativity to avoid it. If it can't be avoided at all, there is no problem provided the readers know what you are talking about.

My understanding of the journal style guides I've seen is that once the acronym had been introduced you may use the short form after that. There are often situations where you might use the full version after this:

• Sometimes you are required to use the long form in figure captions (at least at the first occurrence per figure) .
• Sometimes the term is really needed at the beginning of a sentence and it's often regarded as bad form to start a sentence with an acronym.

Remember that clarity must come first. This can easily mean that the long form is required after the acronym has been introduced.