I have that ability too but i don't know how to control per se
If I remember a dream when I wake up, i can probably remember it a couple days later too or further. However, I merely keep a dream journal for entertainment purposes.
I have a really good memory, not sure if it helps, but I remember note-worthy dreams almost indefinitely.
If I'm not woken up suddenly and forced to react (e.g. an alarm, or someone shouting "Good morning!" and me having to mumble something coherent back), I will remember my dream for pretty much ever, just like a regular memory.
It gets harder to distinguish real from fake when I start doing so much of a real thing, like full-time work, that I start dreaming about it. I have dreamt of a shift of work before, and woken up only to be completely dismayed that I now had to do it again, and I had to figure out whether or not I had actually done X with my boss, or spoken to another person about whatever, or if I had completed some task.
I use a lot of my dreams as material for creative work. This probably helps me retain them, since they become "useful" and "important".
Do you ever remember your dreams while you're dreaming? I've started doing this, and it's five kinds of disorienting. It's the closest I've gotten to lucid dreaming.
I randomly remember dreams from all across my life, the details usually being small but varying and I get a lot of repeats but it's probably triggered at least a few hundred different ones by now.
I can generally remember my dreams just fine without a journal. I like to keep a journal anyways though, just for the sake of writing them down makes them easier to recall future ones, I guess it puts dreams as higher on my mental priorities than before, I don't know.
Like other people though I do tend to dream things and forget whether they actually happened or not, usually just minor conversations with people. I've come up with a few inside-jokes with my dream-friends before, and have left my real friends confused when I try to reference it later. A few of them have turned into real inside jokes though so I suppose it all worked out!
I can remember bits and pieces of my dreams. hell, I even have ome parties with my dream denizens, all of us speaking our own, unique language and writing our unique code. It got so cool, i actually took a piece of paper and wrote down the alphabet we came up with. hell, the friends of mine who know about my dreams want to know about said language!