There are three levels of ticket prices in Italy - Super Econ, Economy, & Base. The SE and E tickets are limited in number per train. Early or late day trains will have more available than mid-day trains. But numbers are fixed so once sold there are no more. SE and E come with restrictions. SE - no change period and E with one change credit towards the next ticket. Miss a train with a SE, E ticket and they are dead. The Base ticket is exchangeable, etc. SE can be very cheap but sell out quickly around the 90 day mark.
At this time most of the discount tickets for July travel will have been sold. A few could be left for odd schedules or very early/late trains. So, if SE or E fares are not available on-line, then I would wait till you are in Italy. If you buy a couple of days early you should be fine for getting seats together or at least 2 and 2. Also found the Italians are pretty good (tourists not so much) about switching seats. Trains rarely, if ever sell out.
The one exception to all of the above are the Regionale trains (R). No discount, did not buy on-line,, one price, and no reserved seats. These trains never sell out. Buy a ticket, validate it, get on. No seats available, wait till they are at the next stop. Regionale trains are slow because they hit nearly every station. But if if not in a hurry, they are kind of fun (for awhile to ride). You see the locals and the country side and lots of small stations.
Train travel is great in Italy. We have ridden a few thousand miles and we are still alive.