In principle there is no reason why you get this change of frequency. There are two causes of frequency drift :- 1, thermal, does the frequency drift back to where it is was?, does it change with temperature?. The other, 2, is sensitivity to power supply voltage, the 555 is very susceptible to this. An on board regulator could cure this as it might be that your bench PSU has a varying voltage output after switch on. Astable oscillators might suffer the same effects. You could try a wien bridge oscillator, which depends to a less extent on the power supply variations. A proper LC tuned circuit or a crystal oscillator are the ultimate for stability, providing they are designed and built with stable components.
Frank