Basically merge mining works like this:
When a miner mines a block for LTC, it will get LTC rewards. If he is merge mining for VIA, that solved block hash is accepted by VIA blockchain as ProofOfWork (not 1:1, depending on the hash complexity, e.g. solving 1 LTC block grants you 3 VIA blocks - this is ultra simplified, just for giving a rough idea!).
So even if the reward from VIA goes near zero, it is actually still cool for a miner to do merge with VIA cuz he doesnt have to use any resources to get a small additional reward (plus the fees).
When a miner mines a block for LTC, it will get LTC rewards. If he is merge mining for VIA, that solved block hash is accepted by VIA blockchain as ProofOfWork (not 1:1, depending on the hash complexity, e.g. solving 1 LTC block grants you 3 VIA blocks - this is ultra simplified, just for giving a rough idea!).
So even if the reward from VIA goes near zero, it is actually still cool for a miner to do merge with VIA cuz he doesnt have to use any resources to get a small additional reward (plus the fees).
Yes, I understand what merged mining is, what I don't understand is why solving 1 LTC block grants you 3 VIA blocks since both coins are using the same hash function, but lets say this is by design, maybe this has something to do with the difference in block-times.
When the mining rewards are getting very small I don't think that miners are very interested in keeping the coin alive when they have to make changes to their code-base to keep things working. You already see this happening right now, it takes very long before f2pool starts signaling segwit for VIA, it gives me the impression that it has not a high priority for Wang Chun (if any) otherwise it would have worked already (assuming the bugs in 0.13 are solved by now).
That "3" was just an example, I have no idea how exactly that is setup between VIA and LTC, just to show that it is not 1:1.
I am not sure why the miners should loose interest. There is no real work on their side (they dont have to adjust their software, VIA does and gives the compiled code to them). Yeah, they have to install it and rollback if it has errors, buts that about it. Not bad for some free extra money, even if it is only transaction cost and no reward I feel.
