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They must have valid reasons for doing so. After all Bittrex earns when people trade and not by delisting coins

Nope, not necessary, they could have shady reasons too ;-) And there is nothing wrong at all with Metal... they simply do not want to support their competition LOL. Metal will go up without Bittrex too ;-) Check it up: https://steemit.com/crypto-news/@cryptoclick/breaking-news-re-metal-token-developments

Do some research on the coins they don't look legit to me so it's probably for good reasons they're being de listed. Here is my brief summary;

Every DGX = 1 Gram of gold. (Bold claims for an ICO)
MTL is also an ICO could be legit but I'm not sure
TRIG - Last post on twitter was in November

What is MTL? I do not fully understand this whole "Proof Of Payments Processed" as a means of securing a network.

MTL is a cryptocurrency for the Metal Payment processing platform which will speed up the cryptocoins mass adoption by providing a clean, friendly interface coupled with multiple membership incentives.

This is quoted from my post here: https://steemit.com/crypto-news/@cryptoclick/breaking-news-re-metal-token-developments
You are invited to read it and... get some Metal tokens

if they have decided to delist a coin it is more then likely because the team behind the coin is either having trouble or doing something shady.

What will happend to my coins, if I don´t sell them and they will be delisted? Do I lose it?