H&R is really not out of business, I just spoke with them on a warranty repair. They are moving to Huntsville, AL and should be back in production in 2016. Of course, this really isn't the same H&R 1871 is was (its Remington) and they have been saying they are moving for two years.
I've owned Handi-Rifles in 223 Rem & 30-30 Win and they shot bad enough that I just got tired of messing with them and sold them. I owned a special run 444 Marlin before they were a cataloged offering and it was a good rifle. I recently, in the last month, purchased a 35 Rem/444 Marlin combo from Bud's(a Remington build) and everything about it was bad. Before I shot it, just exercising the hammer/trigger to get a feel for it (not dry firing it), the trigger broke. The bluing is almost nonexistent and the tooling marks in the barrel are crazy. It was sent to a gunshop in Dallas and they fixed the trigger under warranty but honestly, I not going to keep it. A fellow that hunts on my place showed up with a 22 Hornet that was fairly new and after shooting half a box of 50 on my range, he took it back to the shop he bought it from and added money for a Mini-14. The H&R shot terribly and the finish was very, very basic.
I had a CVA Hunter Compact chambered in 35 Rem and it was finished product. I should have bought the full size model as I'm a big guy and it was available but didn't. The Compact is a small rifle so I ended up giving it to my friend mentioned above reference the 22 Hornet. He really likes the rifle and the 35 as a great Texas big game cartridge. I looked for a CVA Hunter replacement in either 35 Rem or 44 Mag but never could find one. CVA says that they are coming in but are gone fast. They are build in Spain.
What about the Rossi Single Shot? I have a couple of the Braztech built rifles, a 308 Win & 44 Mag plus a 12 gauge Slug Gun. I think there is a difference in quality between Amado & Braztech built with the later being better. I had an Amado Rossi 7.62x39 and really liked the cartridge but it had the common light primer strike problem that was typical of this generation of Rossi Single Shot. I killed this hog a week ago Friday with my Rossi 44 Mag Single Shot, it is my backdoor rifle (the hog was in my yard).
Here is my take on the rifles having purchased the various competing brands. The CVA Hunter is the top of the heap. Nothing negative about it other than finding one. Finish is better than what this type of rifle has led us to expect. Don't know about support because the one rifle I purchased is still going strong. Without a doubt it is the best looking of the three. Sweet 3 1/2# trigger. Very compact hammer allowing high ring use with the POA 1.5" over bore. Comes with CVA rings and a card for open sights. If you want them, you send the rings back with the card.
The H&R based on my very late manufacture of rifle is rough. 6# trigger. Hammer radius requires extra-high rings which places the POA 2" over the bore.The stock was synthetic but a very rough finish with a cheap camo paint? Bluing nonexistent. Both barrels have tooling marks. As I remarked, the rifle is still being supported for warranty work.
The Braztech Rossi has deep bluing with very good metal work. Tight hammer radius allowing high rings with the scope POI 1 1/2" over bore. The open sights are synthetic, not metal, but are fiber and are actually quite good and easy to adjust. Sweet 3 1/2# trigger. Synthetic stock molding better than H&R, almost as refined as the CVA. Rossi used sling loops rather than quick detach studs so that is a negative in my book. The butt stock stud is molded into the stock so any wear worries me as there would not be a fix other than a stock replacement. Believe or not, I just received my 308 Win via FedEx a few minutes ago. I had a forearm/barrel fit issue that I felt that Braztech should address and they did. Out and back to Miami was about 10 days. Rossi did drop the Single Shots from their product line at the end of 2014.
You might have to buy what you find given the availability of these top break rifles.