I've frequently enjoyed this word, and now I have more cause to use it, given my recent lapse in posts.
Remiss is a derivation of remit from the Latin "mittere", which means "to send", and with "re" means "to send again", or more colloquially, "to send back". From there, to went from the tangible, of sending back something, to putting something back to its original condition as an extension of if the thing never needed to be sent back, applied to both physical and mental conditions, and then to pardoning as the ultimate way of putting a mental condition back to its original state. So, what does this have to do with being slack or relaxed or finally to "being neglectful of a duty"? Must have occurred in the Middle Ages... Yes, of course! Somewhere c. 1400, late Middle English created the word remiss from "remissus", the past participle of remittere, and as with so many words from this time, gave it some random attribution. Well, in the spirit of not being remiss, in any definition or etymological derivation, I'll give it a shot to reconcile this meaning.
When last we left the etymology of remit, it was to put something back to its original condition as if it had never occurred. And as long as we're going to pretend that something never occurred, let's just say that we're not being too strict in the application of the thing sent. From there, it is just natural extension to say that the failure to strictly apply the force or effect is carelessness or laziness. The requirement that there be a duty derives from the intent to have a force or effect from the thing sent. By a second route, there is the natural inference that the thing which was theoretically "sent back" had no force or effect. Now, of course, that requires a change in perspective from the recipient to the object being received, but from the lack of force or effect, which is a latent definition for remiss, it is an easy step to not having enough force or effect when such was expected, to simply being careless or lazy. In both cases, the lazy inherent meaning also gives rise to a sluggish or slow meaning, but the speed of the force or effect, or lack thereof, has no bearing on the etymology of remit or remiss, and is an inappropriate extension. Remiss is just about a failure to act when there is a duty to do so, at whatever pace that may be. That a failure to have force or effect may not be observed or acknowledged for some time is what gives the appearance of being slow or sluggish, but that's a relative perception based on context. In litigation, Plaintiff's counsel's failure to answer the emergency motion the day that it is received is just as remiss as his failure to complete discovery within the nine months provided by the tracking order.
So, in other usages... Her electricity will be turned off if she is remiss in paying her bill. My cat will meow at me if I have been remiss in feeding her enough roasted chicken. And finally, I have been remiss in posting entries to this forum. I fear that with my rehearsal schedule in the Spring, remiss may bleed into egregious. Bear with me, please!