Their warranty period is only 2yrs, but they've always been good about fixing older rifles, even the current owner, one member sent a second hand barrel in to be fitted earlier this year which they did, all he had to pay was shipping which I would expect they would want you to cover since it's an ejector which makes it a few years old. Have you read the Handi Basics 101, made sure the latch/shelf are clean and dry? Shot it without the forend? Those two things probably account for 90% of the problems and are easily fixed.
I have four H&R 243s, two Superlights and two Ultra bull barrels, they either like 90gr and lighter or 95gr and heavier, 95gr Fusions and 100gr Powershoks shoot good in one of the Ultras, the other liked 80gr Rems before I rechambered it to 6mmAI which shoots 87gr Vmax handloaded well under 1". The Superlights like 100gr Speers handloaded with H4895, 80gr Rem ammo shoots fair also, <2" as long as you don't shoot when the barrel is hot. If you haven't done anything to the forend, I suspect it's too tight which is easy to fix on a wood stock, a little harder on the syn, but there are remedies for both in the FAQs that don't take much time, effort or skill. I'd shoot it without the forend with the best shooting ammo, if it shoots good, the forend needs work, it shouldn't fit tight, just tight enough to stay on without the screw is where I start on a new rifle, usually that's all I need to do, usually a pressure point added to the forend tip helps too.

Tim