Well, it is not uncommon for the target to just randomly disappear. The most logical reason would be NPC's around - however, if you're sure there are no NPCs around, then it may just be the mechanics of DexNav.
According to this source (under Approaching), it states that Pokemon can disappear for no apparent reason when the player is approaching the Pokemon, thus allowing it to warp to another spot. It is good to note that the mechanics of DexNav is based around a radar system - and because of this if the Pokemon is outside the radar (not necessarily the problem) or it's warped to the center of the radar (where you are standing), the Pokemon will run away.
In other words, where the Pokemon warps afterwards in chaining with DexNav is all due to randomness (a random spot within the radar). If you are standing in the desired spot where the Pokemon wanted to warp to, you are preventing it from moving there thus allowing it to run away - and this may be the no apparent reason you are looking at.
Also, a long duration from using the menu or anything acting as a "pausing" during the chain will have the Pokemon run away.
Since you also mentioned shiny hunting at the end of your question, a similar question was asked and it states DexNav shiny hunting usually reaches your 50% mark anywhere between 120-160 steps, but there will always be a chance of failure, regardless of how far you proceed (so this is a very tedious, patient task). Doing it in water and in caves is definitely a pain since random water and cave encounters break it.
Nonetheless, hope I helped! :)