Okay we checked this out and the issue is actually related to woocommerce subscriptions .
When you are using woocommerce subscriptions plugin and its wplms addon the normal function which adds user to course is prevented to do that and the control is given to subscriptions .
The access to course is released based on woocommerce subscriptions then ,
In your site yes we did found the order by that user but we could not find any subscritions for that user .
http://prntscr.com/m7yveg
We even found that there was no order for that user was showing in front end to the user itself .
Therefore no subscription -> no access to course is given .
I would also recommend you to disable the woocommerce autocomplete orders plugin which we told you to install .Before we did not knew you are using woocommerce subscriptions .
Woocommerce autocomplete orders plugin create issues with woocommerce subscriptions .
Please make sure that subscription for the user is created/renewed when order is created.