Recording Live TV in progress should (and does, for me with H3 and even legacy DishPro models) work like this:
1. If you have been tuned to the Live channel since BEFORE the current program started (as in you first tuned to the channel with a show, and then later that show ended and another new show started), pressing the REC button will save and record the ENTIRE newly started program--from its beginning--From any place in the show BEFORE it ends, provided you were tuned to that show BEFORE it started on that same channel. This means the entire buffer containing that current show airing will be saved in its entirety.
2. If you have tuned to a channel with a show already in progress, then pressing the record button will save a recording ONLY from the moment you press the record button. In other words, if you tune to a show already in progress and wait, say, 10 minutes before you press the Record button, then you will ONLY get a recording from the moment you pressed record and the previous ten minutes buffer is purged and NOT saved as part of the recording.
3. If you have tuned to a show already in progress, and watch that show for some time before realizing that you would like to save the content you've already watched along with the remainder of the show, then you can REW back as little (say you just want to save as far back as a few minutes before, but not more than that because you just want to pick up where you left off for later viewing and don't need the entire buffer of what you've already watched) or as far back as the entire buffer, and then press Record. That will save the a recording from the point you have REW to--including the entire buffer if you REW all the way to when you can REW no further--and to the end of the scheduled show time. *Remember, if you were already tuned to that channel BEFORE that show began, then just press RECORD (as stated in #1), and that will save the entire program. You don't need to monkey around getting REW to just the right spot that is the start of the show.
4. If you tune to a show already in progress, and you would like to see in its entirety, rather then a sloppy or incomplete recording, look for the message on the bottom right of the screen that states, "Press Select to see this show from the beginning," and press SELECT while the message is still displayed, and you are offered either the entire show as a (free) VOD or a list of repeat broadcasts ("Showtimes" button will present a list of subsequent showtimes of the same episode for recording) of the very same show episode or both VOD and later broadcasts in the next 7-8 days. You chose which you prefer (I often pick BOTH--one at a time--VOD and later repeat broadcast to cover my bases). Also, if easier or you miss the message to watch from the beginning, you can press the INFO button and you should see some options near the left bottom that often (but not always) include VOD or repeat broadcasts as options so that you can see the entire episode from the beginning. Of course, you just move the on-screen selector onto a the list of repeat broadcasts and select the one you want to record and the timer is set automatically. The list will include if the showing is in HD or SD and on WHICH channel because a few channels are offered in both HD and SD such as Disney Channel and the premium movie channels.
There are a few times when the VOD option for a show/episode is not offered in the INFO screen or via message, but if you manually search the VOD, that episode is, INDEED, available to VOD. It is an annoying quirk of the Dish VOD, so don't assume that just because it is not listed as on option in the INFO screen that is isn't truly listed and available on VOD.
5. Lastly, if you tune to a show or series already in progress and there are no other options to view from the beginning (VOD or later repeat broadcasts), then I just select "Record Seires" from the INFO screen in case the show airs after the 7-8 EPG period, and often it records the same show/episode fairly soon, but there are a few times when that show/episode may not air for weeks or even months, but the DVR records it for me to watch from the beginning. Also, the VOD library may add that show/episode some days or weeks later from when you first viewed the live broadcast in progress, so keep checking/search VOD persistently.
I often use #4 because I don't always know in the first few minutes if I want to see a show in its entirety when I channel browse, but I always take a notice of the "Start from the beginning" on-screen message.
I hope that makes sense. There are a lot of things the Hopper or other Dish DVR's do that are not documented because features are added over time and known mostly to power users. Good luck.