That comes up a lot - but it's not really compatible with what we see in the show. Transporters have a MUCH higher resolution than replicators, meaning that if you wanted to store a pattern long term you'd need an impractical amount of storage space. They literally needed all the computer storage on DS9 just to hold the neural patterns of five people, and had to reconstitute the bodies on the holodeck to be driven around like meat-puppets to store the rest.

The closest you can get to long term storage of a transporter pattern is by constantly cycling the subject through the buffer - basically beaming them out into their own transporter. It's a pretty clever idea because lets them use the outgoing beam as external storage, expanding the effective size of the transporter buffer to be arbitrarily large. But it's risky since every time you send that signal out, you're going to get a little bit of data loss as it travels back. No one really cares if they lose 0.00001% of their body mass in a normal transport - it's probably nothing the body can't deal with on its own. But when it happens billions of times in a row without any kind of break...

Well, the odds of you rematerializing with a heart that looks like a block of Swiss cheese start getting hard to ignore.