Theoretically, using the same address over and over for transactions reduces their security. However in reality this shift is so insignificant that you don't need to worry about anyone compromising your private key as a result of it. Reusing an address is a security issue if you have a weak random number generator, as was an issue with the Android Bitcoin Wallet.
If you're interested in knowing why using the same random number in two messages is bad, you can read about ECDSA (ecliptic curve digital signature algorithm) here:
https://en.bitcoin.it/wiki/Protocol_specification#Signatures