Italian Train Split Ticket Question

I am only guessing that the problem is related to the up-dated schedules that may not be fully loaded at this time. The change date is roughly June 12. You first schedule is just not completely loaded yet. If the trip is acceptable to you there is no reason not to book it. I cannot access italiatren just now because it is down for maintenance.

When I just look at the Roma Termini to Bologna Centrale 10:35, it shows "Not for sale". But the 10:20 is available with Super Economy tickets. So you get to Bologna 17 minutes before your preferred train, giving you plenty of time to make the connection to the Regionale to Ravenna. You can buy that ticket when you get to Italy.

You can split the ticket without any problem. The Bologna-Ravenna will be a regional train, you can buy that sector in Italy (prices for this sector are fixed).

I assume that means it's full or not available.

There is no need to assume, if you hover the mouse over the barred cart without clicking it, the desktop version of trenitalia.com shows the reason a train can't be booked.
Many FR1000 high speed trains leaving from Rome in the morning seem to be sold out on the 19th of June. As the FR1000s always go to Milan after calling at Bologna, I wonder if there is some big concert at San Siro stadium or something like that.
Regionale trains have no reserved seats, hence they can't be full.

The 10:35 is not showing on the Duetsche Bahn schedule, which might mean it is not officially scheduled yet. I'd go with the 10:20 and buy it now while it is still 24.90 EUR.

Ignore the DB schedules, they do not run any of those trains

The FR1000 leaving at 10:35 was scheduled and uploaded on the system months ago and now it's labelled as sold out. It's not a regionale, the timetable change of June has almost no effects on the scheduling of high speed trains.
If a train wasn't officially scheduled the Germans wouldn't know anything about it; they can only access the official timetable with trains that are scheduled to run, like dozens of indipendent train apps. DB simply prefers not to show trains that Trenitalia says to be sold out.

Thanks for all the great advice and especially for the hovering bit. June 19 is a Monday. I should have mentioned that I will need to leave after 11:00, but the advice still applies. I have my CC turned on for purchases in Italy in Euros until midnight tonight, so I'd better finish this up.

Just as a note -- we booked seats Bologna-Firenze on the Bologna-Roma train last week (at Bologna station) and got some of the last 2nd class seats. That train was full! (Met some people who had tried ten minutes later and only had first class available.)
Bologna-Ravenna, as noted, is a separate regionale train.

I hit a few glitches last night, but all was resolved today, so I am now the proud owner of train tickets from Rome to Ravenna and from Ravenna to Venice. I'll buy my tickets locally from Venice to Padua to meet up with the RS Village Italy tour.

Once again, thanks everyone for your help and for spurring me on to work around the system. Incidentally, not splitting the ticket from Ravenna to Venice Santa Lucia was the best option for me.

Buying early certainly has its rewards. Total price from Rome to Ravenna was 37.25 €. For Ravenna to Venice it was 22.25 €.