As you already supposed, and the other answers also do point out, "abhanden kommen" can be translated as get lost. But since you asked for the connotations I want to add some information concerning this aspect of your question.
"Abhanden" is the contrary to "vorhanden", which means "present". The literal translation of "vorhanden" would be - as you already might have guessed - "before hand", but it does not mean beforehand, but rather at hand. So "vorhanden" is something which is present to be used, to be taken in hand. And "abhanden" is quite the contrary "off hand", absent. (Also see Pfeifer)
For the connotations of "abhanden kommen" the meaning of the prefix "ab-" is significant as well. In german "ab-" means something like "away" or "off" (see the first meaning in https://www.dwds.de/wb/ab-). To get a taste of the prefix you might find it helpful to take the following examples onto your tongue:
- "abgeben" - to cede, or: to emit
- "ablehnen" - to refuse
- "abtreiben" - to abort
- "abstoßen" - to reject
So, we already have something. But when it comes to "abhanden", the third meaning mentionend in https://www.dwds.de/wb/ab- - the meaning of a gradual process - is also relevant:
allmählich, nach und nach. Beispiel: abblassen (to pale out), abkühlen (to cool down), abmagern (to macerate), abstumpfen (to deaden), abzahlen (to aquit [a debt]) [english translations by me]
In the term "abhanden kommen" "kommen" as a verb of movement even stresses the latter connotation of a slowly, gradually change. The example of Erich Kästner's poem Roland Illig cites in his answer makes heavy use of this connotation: Even if the speaker states that the love of the both got lost suddenly ("plötzlich"), the use of "abhanden kommen" suggests that this was in fact a steady process with only its result being sudden to the both. (I would argue that the contradictory tension between the processual connotation of "abhanden" and the "plötzlich" (sudden) is marking the perspective of the speaker who analyses the lovestory of the two from the outside).
I think that in Rückert's Ich bin der Welt abhanden gekommen the use of "abhanden kommen" shall allude the concept of a slow and gradually process (a struggling I would say) as well.
Of course all this is merely interpretation and thus open to dissent. But I think that's partly due to the question asking for connotations.