While it may not be necessary, you really should have a pull-up resistor from RESET to VCC. 10K ohm is a good choice.
Which ATtiny45 model are you using? The minimum voltage for the non-V model (0 – 10 MHz @ 2.7 - 5.5V, 0 - 20 MHz @ 4.5 - 5.5V) may give a short battery life / cause problems when running from a 3 volt battery.