Pedro,
Theoretically, that is possible. A router, just like any other computer, may have bugs in its operating system code that can cause, for example, more and more memory being allocated to various processes without being returned to the operating system (a so-called memory leak). In the end, the router ends up with no free memory left. There may be also other possible bugs that can, over prolonged periods of time, lead to certain system resource shortage that will ultimately result in low router performance.
There are also ways in which router can slow down over a period of time without any bugs in its operating system. Consider, for example, the memory allocation process. Different processes allocate different amounts of memory, possibly scattered over the entire address space. After a certain time of operation, the free memory blocks may become so fragmented that it is difficult or even impossible to find a free space of a certain size (the so-called external fragmentation). Using some kind of virtual memory may allow splitting a block of process memory into several different locations of the physical memory; however, this naturally results in more work for the router's CPU to do and logically, in a possibly decreased performance. Note that the router has done nothing wrong here. It is very similar to hard disk fragmentation.
Notice that what I have indicated here is very general, and relates to two possible sources of problems: software bugs and software design. In any case, rebooting the router "just to be sure" is simply an unfounded and totally unprofessional practice. It is like giving patient a prescription without actually knowing whether he is ill at all.
I would personally discourage from rebooting the router from time to time if there is no persuasive evidence that it is going to solve problems that are already detectable and visible. Rebooting the router just so may be trying to solve problems that do not even exist.
Best regards,
Peter
