You say "When the device is about to transmit the signal" and use the word "sudden" which implies things are going fast, so we can rule overheating.
Check 7805 regulator input and output voltages with a scope while doing your transmission test.
- Output voltage falls, but input voltage stays strong: add more capacitance at the output.
- Input voltage falls too: add more capacitance at the input.
Some modern fast LDOs are happy with 1µF ceramic at the output. But 7805 is quite an old design, and as such it is slow to respond to fast current changes. Thus it needs capacitance on the output to smooth things out. Maybe your DC-DC is slow to respond also, but this is less likely (do the above measurement).
Since a 100µF 25V capacitor costs 5c you might as well put one on both sides.
You'll want to keep ESR under 2 ohms to reduce voltage sag due to 100mA current spike to a reasonable 0.2V maximum. Since most general purpose caps have tandelta around 0.1-0.2, this means 100-200µF or more. A 10µF cap would have too much ESR to be of any use on the output.
You could use a low-ESR cap if you have'em, but then you'd have to worry about stability and such, so basically just reach into your parts bin and grab any general purpose electrolytic that's big enough and fits. It won't hurt if it has more capacitance than required.
Also if the thing will sit outside in the cold, remember that capacitor ESR goes through the roof at low temperatures, so in this case you might want to oversize the cap or use something a little more evolved like Panasonic FC. Or just stick a 10µF ceramic in parallel instead of your puny 330nF.