|Don't ask to ask, just ask|
Your tutorial was automatically, not deliberately dropped from the list. As you noticed, new tutorials are automatically listed in a section called "Tutorials added in the last week." This section is automatically added to the end of the existing Tutorials page when served by the PM engine.
Currently, the general process for getting a Tutorial added to the permanent list involves Consideration. Generally, a monk with consideration powers will notice the new tutorial, consider it with a reason similar to "Promote to Tutorials? (Edit eq Yes, Keep eq No)"1 and wait to see what other monks feel about making the new item a permanent part of the tutorials list.
After a decent period of time, e.g. long enough for a janitor to get a sense of how the promotion voting is going, the node will be added to the Tutorials source or removed from Consideration without further action.
It's not a formal review process by any means and, like many other editorial decisions on the site, is based more on the experience of the janitor in question than any hard and fast rule. As with other nodes, we try to err on the side of generosity than elitism. Sometimes, simple mistakes get made.
In your case, it appears that no one considered your node for promotion2 or that I made an error when recently revamping the Tutorials page. If it was the latter, then I apologize.
I promoted jeffa's tutorial after only a few days primarily because the promotion voting was clearly going in the that direction and it it had a high enough reputation that it was clearly valued by the community at large. (Also, his tutorial was intended to replace an earlier one based on a now deprecated module; thus, his was more of an updated tutorial than brand new material.)
So, no. You do not have to be a high level monk to get a tutorial listed permanently; however, some general advice for all would-be tutorial writers might include:
Update: P.S. Looks like VSarkiss types more quickly than I do. And more concisely. ;-)
1 - Yes, it's a hack. We may change that at some point. If there's time and we manage to get everything else done that we need/want to do.
2 - This has now been corrected. We'll see how the promotion voting goes.