For that I used R1=9.8kohm, R2=17.6kohm, and C=820pF. At the beginning, the frequency I measured was right at 38.2 kHz but as time passes by the output frequency started scaling up for as much as 2 kHz. I mean, the frequency increased by 2 kHz in less than half an hour. I tried to change the type of the capacitor just to make sure that the capacitor was ok. But I didn't get a constant freq. either. Maybe it's with 555 timer that makes it behave like that?
If you're building an oscillator for communication purposes, C-charge based oscillators won't do – aside from a very few speciality devices, capacitors are rated for 5%, 10% or even 20% tolerance. So I'd say your circuit operates well within the physical boundaries of what your components offer.
I'd strongly recommend just getting something that has a trimmed internal oscillator – that something might actually be an 38 kHz oscillator, or, even simpler, a microcontroller generating 38 kHz with e.g. a PWM unit. This option sounds twice as reasonable considering that when communicating over IR, you most probably already have some digital logic!
May be a shot in the dark, but could this be due to dc bias on the capacitor lowering its capacitance? You say you tried changing the type of the capacitor. Did you change it something other than ceramic - such as a film capacitor, which experiences less effect from dc bias?