Q:

How many times can I submit my app to iTunes Connect? 

I recently have been submitting quite a few reviews to Apple, and I wondered if they might get annoyed with the amount of times an app is called for review.  I have not approached this limit yet, but I wanted to make sure I do not annoy Apple's reviewers. 
How many times can I submit my app to iTunes Connect for review?  Is there a certain amount of times per month or week? 

A:

I'm not aware of any documented maximum number of times you can submit an app for review (source: App Store Review Guidelines). 
The Review team will take the most-recent review request and start their review process, based on my experience over a few years.   When you submit a new version for review, the previous version is no longer eligible for review. 
The only time you need to be concerned is when the review has already started (you've been notified that it's started) and then you want to do an update.   To avoid this situation, just be sure you really want them to do the review and your app is ready before you tap the 'submit' button.