On Latin and English and Mappings

It's illuminating how much of another language you can pick up if you've got a reasonable grasp of a related one.
And in the case of languages, there are a whole heap of related ones.
Now, I'm not talking about reading books, or even grasping full sentences.  But pithy quotes?  Not a total write-off.

The spark for this post was a Latin quote by a mate,
"Omnia mutantur, nihil interit"

But the origin of this post can be found some time ago.

When looking into the artificial language Ido, I came across a handy table describing words and the closest match in several languages.
One example was the noun, "kavalo", which in english means "horse".  So far, so confusing.  But the closest match shows that we can (imperfectly) map it to the concept of "cavalry", and this is indeed how I remember the word (along with the fact that nouns in Ido end in -o).

Fast forward to this evening and we have this latin phrase "Omnia mutantur, nihil interit".  Now, I'm not of an age where I learnt latin in school.  I'm also not of the bent that I decided to learn a dead language of my own accord.  I must admit I'm fond of the occasional latin phrase or word (readers will recall my hunt for ex-situ's antonym) but, all things told, I really don't know any latin worth mentioning.

The phrase was posted without an english translation, perhaps because it was assumed to be well known enough to not require it.  Alas, that was not the case for me.  And yet, looking over the phrase, mappings immediately became evident.
Omnia: omni- (prefix for all, everything omniscient, omnivore)
mutantur: mutate (to change)
nihil: nil (nothing)
interit: ... ( ...? )

So close, stymied at the last. 
Now, I'm vaguely familiar with the english translation, but even with the first three words I was unable to complete the phrase and had to resort to google.  "Everything changes, nothing is lost" for those of you still wondering.

So the question becomes, where is the link between the latin "interit" and the english "to lose, perish, decay"

The closest I can get is intermit, and that's not very close at all. 
Anyone?