Can advertiser retarget my traffic?

Say I drive traffic to an offer via my affiliate link but the visitor doesn’t convert.

The advertiser who owns the product page cookies the visitor I sent and then retargets them later (on facebook or other channels).

If that visitor later converts from the advertisers retargeting, do I lose out on commission?

Of course you do.. but what can you do about it? it's part of the game.
Unless your lead converted on that very same visit they don't "owe" you anything,
But usually companies respect good affiliates and tries not to screw around with affiliates like that. they will just lose traffic and good conversion rate if the do.
you should know what's your average conversion rate and if the numbers doesn't add up then you can tell that the other side is playing you.

If you are a very high valued affiliate you can usually make some agreement with the company, extended conversion period time etc..

Off course you will lose commission.

You can manually check if advertiser is dropping any cookie.