Instant coffee may not be lost during processing and just have a lower caffeine content simply because less coffee is used in making the cup. One tablespoon of instant coffee in 8 oz of water gives a brew with TDS of .75%, about 30 - 45% lower than the recommended TDS for coffee. https://www.scaa.org/PDF/resources/golden-cup-standard.pdf An 8 oz cup normally brewed with one tablespoon and containing 55 mg of caffeine, would contain 80-85 mg when brewed with matching TDS.
At similar TDS, instant coffee might have less caffeine, because it is often extracted at higher temperatures and pressures than drip-brewed coffee. This would make it easier to extract more solids less soluble than caffeine than in normal conditions, resulting in an extract with a lower caffeine to total solids ratio than in drip brew.
In regards to process related losses:
If freeze drying, caffeine could be lost due to sublimation. However, the rate at which it does is might not be significant, since caffeine seems to be normally heated above 100 C, in a vacuum, when intentionally sublimated.
If the coffee was spray-dried instead, caffeine could be lost with evaporating water vapor. A major loss of caffeine during roasting has been attributed to this. http://www.sciencedirect.com/science/article/pii/S030881461100762X