There are some strange entries in the flight schedules beginning late January. Normally flights are either 12345, 123457 (aka "x6"), every day, Saturday only, or Sunday only. Adobe's pdf reader finds 354 instances of _4_ (Thursday flights that don't operate Wed or Fri) in the "All Cities" pdf schedule for 24-Jan through 12-Feb. (That would be at most 177 different flights, probably far less due to some or many having multiple segments.) If you want to see examples without downloading the All Cities schedule, the PHX schedule for same time period lists seven flights that are Thursday only ("___4___"), three that are Wednesday only, and one that is Wed/Fri only.
What this appears to be is cases of flights that are not supposed to be "published, scheduled service" being incorrectly coded one or two days per week. In the cases I have checked, the data is consistent across the pdf schedules, the online viewable schedules, and the online booking engine, so the errors must be in the way flights are coded in the master database. This probably has no effect on what flights an RSA might offer you by phone; their front end to the reservation system lists all flights, not just "published, scheduled service."

Some interesting insights into "unpublished" service can be gleaned from these schedules.

• Often they are lousy connections that someone would only book under unusual circumstances (nothing else available; the only way to redeem an award that day on that route; want to spend an extra hour or couple at a mid-point; better departure or arrival time match to available ground transportation; etc.) Example: earliest published service PHX-FLL on 11-Feb is three segments, departs 6:35a arrives 3:40p (7:05). There is an unpublished two segment flight (connect DEN) departing 6:00a, arriving 3:50p (7:50). Similarly, there is a 1:45 departure connecting in TPA that operates as "published" service on Thu 12-Feb, but as unpublished service most of that week. You can book the 1:45 departure as PHX-FLL on the 12th for a web-only fare of $169; if you book it as an A-B-C instead (any day that week except Saturday), the booking engine will not combine the fares and you'll have to pay more.
• In other cases it is due to violating the official "minimum" connection time. For example on 20-Feb you can book a three segment PHX-FLL flight (MCI connection) (2636/1112). Try to book those same flights as a PHX-MCI-FLL A-B-C on the same date and you'll receive a not enough time to connect at MCI error message.

Given the eye-popping telephone reservation fees web only "discounts" I've seen on some itineraries lately, I'm thinking I might prefer to have the web site booking engine offer unpublished routings, even if those flights remain "unpublished" in the hard copy schedules.

Apologies, ciaobella, I see I left one of the important observations buried in the example in bullet point one. In all cases that I checked, the flights do operate on the same schedule at least five days a week. It is just that they are only listed as published connecting service one or two of those days.

I gotta stop being so brief, it causes confusion.