When your signal handler returns (assuming it doesn’t call exit or longjmp or something that prevents it from actually returning), the code will continue at the point the signal occurred, reexecuting the same instruction. Since at this point, the memory protection has not been changed, it will just throw the signal again, and you’ll be back in your signal handler in an infinite loop.
So to make it work, you have to call mprotect in the signal handler. Unfortunately, as Steven Schansker notes, mprotect is not async-safe, so you can’t safely call it from the signal handler. So, as far as POSIX is concerned, you’re screwed.
Fortunately on most implementations (all modern UNIX and Linux variants as far as I know), mprotect is a system call, so is safe to call from within a signal handler, so you can do most of what you want. The problem is that if you want to change the protections back after the read, you’ll have to do that in the main program after the read.
Another possibility is to do something with the third argument to the signal handler, which points at an OS and arch specific structure that contains info about where the signal occurred. On Linux, this is a ucontext structure, which contains machine-specific info about the $PC address and other register contents where the signal occurred. If you modify this, you change where the signal handler will return to, so you can change the $PC to be just after the faulting instruction so it won’t re-execute after the handler returns. This is very tricky to get right (and non-portable too).
edit
The ucontext structure is defined in <ucontext.h>. Within the ucontext the field uc_mcontext contains the machine context, and within that, the array gregs contains the general register context. So in your signal handler:
ucontext *u = (ucontext *)unused;
unsigned char *pc = (unsigned char *)u->uc_mcontext.gregs[REG_RIP];
will give you the pc where the exception occurred. You can read it to figure out what instruction it
was that faulted, and do something different.
As far as the portability of calling mprotect in the signal handler is concerned, any system that follows either the SVID spec or the BSD4 spec should be safe — they allow calling any system call (anything in section 2 of the manual) in a signal handler.