Sorry for the late reply, been busy with work.
@edpalmer42, I actually needed it, it was the OCXO from my frequency counter.
I managed to fix it, but not before playing puzzle with the pieces that fell off.
After I put it back together, it didn't work anymore, which is when I realized that I lost a few more parts (about 10 components fell off in total). This made me think that this was the original issue and that the parts didn't fell off because of something I did. Most components were barely hanging in there and there was very little (if any) solder on the pads.
Luckily, I had the picture I posted here and it helped me replace the missing components, after which I desoldered most of the other components (including the two chips), cleaned the pads and soldered them back together.
When I was playing puzzle the first time, I accidentally introduced a short, which I tracked to the heating element (a JE 800 darlington). I wanted to remove it, but it was glued, so I had to destroy it to see if that was causing the short - it wasn't.
Anyway, I cleaned up the spot where it was glued on, added some thermal paste and replaced it with a similarly spec'd darlington.
I put it back together just to realize that it no longer reaches 10 MHz, regardless of the voltage applied to the adjustment pin and no matter how hot it got (I experimented by adjusting the opamp divider network that handles the heating).
Eventually, I ended up changing some resistors in a resistor network that, together with the voltage applied to the adjustment pin, was setting the frequency. As a side effect, the adjustment range is too wide so the auto-calibration of my frequency counter is a bit off (by 0.08 Hz), due to the resolution of the DAC used to apply the adjustment voltage.
Thank you all for the support and suggestions, next time I'll open up an OCXO I'll know how to do it properly
Oh, and I didn't sealed it this time. I only closed it and applied solder on two corners - this should make it easier to open if it starts acting up again.
Edit:
@G0HZU, after I heated it up and wiggled it, I used two screwdrivers to pry it open just like edpalmer42 suggested.