The ATtiny13 has numerous settings for clock sources and pre-scaling of these. Keep in mind that the Atmel STK500/AVRISP only is able to program the part using the ISP method if:
The pre-scaled clock source used on the ATtiny13 is higher than 32 kHz.
The pre-scaled clock source used on the ATtiny13 is equal to or less than the selected oscillator settings used by the STK500/AVRISP.