The length of the repeating cycle of a decimal is equal to the order of the denominator modulo 10. Since 7 is a prime number and is not divisible evenly by 2 or 5, the order of 10 modulo 7 must exist. By the Fermat's little theorem, we have $10^{7-1}\equiv 1\pmod 7$. Therefore, the repeating cycle of a decimal with a denominator of 7 has at most $7-1=\boxed{6}$ digits.
