This is interesting to me, as my opinion has always been that the tense should shift backwards to an appropriate tense (in other words, any continuous tense would still be continuous; the same applies to perfect and simple). However, a quick Google seems to yield the result that there are a few situations where one might choose not to shift tense backwards.
(The following website I have never heard of before, but is the highest hit [about 4] that covers this topic when I google 'don't always change tense in reported speech'.)
The website, English Outside the Box, states there are some scenarios where we shouldn't (or at any rate may choose not to) backshift:
1) when something was just said (around the same moment as repeating
2) for scientific facts and general truths
3) for information that is still true