For what it's worth, my own progress on this sentence is:
tapasvina < tapasvinas: GEN SG "poor, wretched"
āyuṣi: LOC SG, NEUT "life, health"
gate: PPP. LOC SG, NEUT "gone, dead"
tasyā < tasya: "his"
``tmā < ātmā: NOM SG, MASC "breath, soul"
bālasya: GEN SG, MASC "boy"
tanvāṃ < tanvām: LOC SG, FEM "body, person, self"
jātam: PPP. (presumably: ACC SG, MASC, also possibly: NOM/ACC/VOC SG, NEUT) "born"
Taking āyuṣi gate as a locative absolute we get - in slightly clunky English, but preserving the original grammar:
"When the life of the pauper was gone, his soul was born in the body of a boy."
[When] the life of the pauper (tapasvina āyuṣi) was gone (gate), his soul (tasyātmā) was born (jātam) in the body of a boy (bālasya tanvām).
Well done Au101, go and have a biscuit... Except: We obviously have the problem marrish has highlighted for us with this analysis, in that jātam, if MASC, is in the ACC SG and is not in agreement with ātman. There are no neuter nouns in this sentence it could be agreeing with. Were jāta- to agree with ātmā I would have expected jātas/jātaḥ.
Anyone able to spot what we're missing, or is marrish correct to suggest it's a mistake?