This is the first time I have ever heard of any issues with any emails not being sent through ANY service. There are a few reasons this may happen:
1 – The emails are not properly set up in Helium 10.
2 – Your email marketing is temporarily (or permanently) suspended by Amazon.
3 – The connection between Helium 10 and Amazon’s API isn’t functioning properly.
As far as other companies that do this, I am sure there are several, but the only other one I have used in the past is Feedback Genius. I ended up spending about $250/month with them at one point though. So, I switched to MBS to SAVE money. lol