Do Lightning Channels have to be resolved before a certain time? I seem to remember that Lightning channels could remain open indefinitely with the introduction of CLTV. Yet, I'm confronted with claims that they time out and coins are lost when they do.  

This seems wrong, as when channels time out they should send back the money, and as I said above, I thought they could remain open. What is it?
I seem to remember that Lightning channels could remain open indefinitely with the introduction of CLTV


I think instead of "CLTV" you mean "CSV" (as in OP_CSV, BIP112).  As far as I know, nobody claimed that OP_CLTV would allow HLTC-style (Lightning) payment channels to stay open indefinitely, but that was definitely a claim of OP_CSV.

An additional prerequisite for indefinitely-kept open channels is segregated witness or another malleability fix.

Although it's a bit difficult to know what is confusing you without reading the source quote and context, I suspect that you're confusing the (1) dispute period for a unilateral spend with (2) a timeout.

When one party to a Lightning channel broadcasts either the current channel state or a previous channel state, there begins a dispute period where the other party can submit evidence proving that the channel was not closed in its current state (that is, it was closed fraudulently).  That evidence is cryptographic evidence that can be submitted to miners, who can add it to the blockchain and have it accepted by full nodes if the evidence is valid.

The dispute period is an arbitrary length of time from the point where one party attempts to close the channel by broadcasting a transaction.  However, there's no point at which either party is required to close a channel, so it's correct to say that channels can remain open indefinitely.  There is no timeout on the channel itself---there's just a timeout whose clock starts when one party decides to start closing the channel.