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I suppose that the infinitive of "possum" once was *potesse, but that the 'e' in the second syllable got lost, so it went from *potsse to "posse". But why did the 'e' in the second syllable get lost?

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It's true that posse as a verb represents a kind of univerbation of potis + esse, but that doesn't mean every individual form does. The present infinitive, in particular, is just the stem pot- with the infinitive ending -se, which is the same as the infinitive ending -re you see in most verbs, tacked directly on.

-se is actually the older of the two forms; as most Latin verbs have stems ending in a vowel (amā-, monē-, tege-, audi-), the -s- regularly became voiced (Very Old Latin will have had amase [amaːze]), and rhotacism regularly turned z into r in Old Latin.
Posse is one of a handful of verbs whose stem doesn't end in a vowel, though, so the -s- was not subject to rhotacism; instead the final -t- of the stem assimilated to it, just as in the forms possum (pot-sum) and the like. *ts > ss is a regular sound change in Latin.

(Latin doesn't much like clusters of a consonant followed by s, so some kind of assimilation actually ended up taking place in most consonant-stem verbs: fer-se became ferre, vel-se became velle, ed-se became ēsse (with long ē because of Lachmann's law; later, though only from the 3rd century CE on, replaced by edere), and only es-se got away with being esse. If there had been any stems ending in -c-, they would have been preserved intact, though written with an x.)

Other forms in the paradigm of posse that aren't just pot- + a form of esse include all of the perfect, pluperfect, and future perfect, in both the indicative and the subjunctive: pot-fuī would yield poffuī, not potuī, and so on. Here, too, the verb wasn't perceived by speakers as literally pot- + esse, but as having a stem pot- that can take "normal" endings.

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    Also the participles: pote-ns not pot-ens
    – Draconis
    Commented Apr 17 at 21:20
  • @Draconis Very possibly, though I feel the model there could conceivably also be absens rebracketed as abs-ens rather than ab-sens instead.
    – Cairnarvon
    Commented Apr 17 at 21:50
  • The older ending of infinitive is reconstructed to be -(e)si (see this, this, this), so I would expect that forms for some verbs mentioned in your answer would be potsi or possi, amāsi, fersi, velsi, edsi, essi. Word-final short i was changed to e by vowel reduction (I think that it occurred after rhotacism).
    – Arfrever
    Commented Apr 18 at 5:20
  • @Arfrever It's hard to date these sound changes firmly, but Roman grammarians had an awareness of pre-rhotacised forms that they didn't seem to have of pre-reduced forms, so I'd place (the completion of) rhotacism after (most) vowel reduction and would reconstruct a stage *-se for the infinitive; to my knowledge we don't have any attested infinitives in Very Old Latin. People mostly do reconstruct an earlier stage *-si based on an s-stem locative, but a *-sa has also been suggested; *-e can reflect almost any short vowel and in verbal forms final *-i consistently disappears.
    – Cairnarvon
    Commented Apr 18 at 15:22
  • @Arfrever Though the infinitive obviously didn't appear in the sentence positions those other forms would have so it would probably have been exempt. I don't have an online source to link you, but I always recommend Weiss' Outline of the Historical and Comparative Grammar of Latin (and disrecommend Sihler's New Comparative Grammar of Greek and Latin).
    – Cairnarvon
    Commented Apr 18 at 15:24

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