One extra point I want to make which is when you add the adverb "regularly" to the sentence, it will skew the meaning which was intended. Consider this:
A- I sent you an email earlier, did you get it?
B- I am checking my e-mail? ----He is logging in to check (now), as I explained in my last post.
If "regularly" is thrown into the sentnce, then it has a slight resemblance to present perfect which means "yes, I have been checking.." .
"I am checking my email regularly but I didn't see your email in my In Box" this is a perfectly good sentence. However,to avoid this cross-tense confusion, I would perosnally choose to avoid sing "adverbs of frequency" like often, usually, and regularly in present progressive sentence.
Example: He usually drinks a glass of warm milk before going to bed. Correct
He is usually drinking a glass of warm milk..... Not a good sentence.
We also have to evaluate the contexts. Sometimes the rules seem to bent, but they still work.
i.e. He sees his doctor regularly. - Fine
He was seeing his doctor and getting check-up regularly. How could he pass away so suddenly?
In contrast with the "warm milk" sentence, the progress sentence worked fine with "regularly".