I didn't find any instance of memory reuse in the Harry Potter books. Once it's in the Pensieve and watched, it's never indicated if it can be taken out again and reviewed.
One counterexample one can use is the first memory of Slughorn, but it could be said from just looking at it that it was tampered with, it was not required to watch it.
Was it possible to reuse memory strands from the Pensieve after watching them? Note that I'm not talking about just storing, but reusing.
Yes
Though it isn't completely clear in the book, I found multiple parts that make it highly likely.
DumbIedore: "I took this memory from her shortly before he died."
Dumbledore most likely saw the memories he took before showing Harry.
This is very clear: Dumbledore told Harry before showing him the messed up memory of Slughorn:
Dumbledore: After we see this, tell me what looks different.
This means that Dumbledore had to have seen it before if he knew that it was messed up and corrupted.
Yes they are.
In Harry Potter and The Half-blood Prince we see Dumbledore showing Harry a memory
of Slughorn
that Dumbledore himself has already used.
Yes. Memories in the pensieve are reusable and capable of being viewed more than once:
In GoF, Harry fell into the Pensieve and Dumbledore's memories witnessing several trials: Igor Karkaroff, Ludo Bagman, and then the Deatheaters that tortured Frank and Alice Longbottom (Neville's parent's). Harry realized that it was a memory and noted the passage of time; so that he experienced not only one memory but several in one sitting. Eventually, Dumbledore joined Harry and removed him from the pensieve, after which Dumbledore proceeded to explain the purpose of the device:
"I use the Pensieve. One simply siphons the excess thoughts from one's mind, pours them into the basin, and examines them at one's leisure. It becomes easier to spot patterns and links, you understand, when they are in this form." -- Goblet of Fire, Chapter 30
Dumbledore also make a comment along the line of having so many thoughts that he finds it necessary to use the pensieve quite often.
Furthermore, it is even possible to alter one's own memories as seen in HBP, when Slughorn modified the memory that he was ashamed of - though Dumbledore said that it was crudely done. And of course, we know that memories can be altered by others, even against one's will or knowledge by using the Obliviate charm - which Lockhart confessed to doing in CoS and we know that Tom Riddle did to his uncle Morphin and Hoki, the old house-elf, in HBP.
If I understood correctly the pensieve is a way of focusing or unfocusing memories from the back/front of your mind. They don't entirely disappear when you take them out, but I imagine for a while they are 'fuzzy' and difficult to retrieve. Unless you watch them in the pensieve, at which point they become very sharp and easier to analyse when viewed.
