'untransportability' is formed in modern English by prefixing 'un-' to 'transportability' (itself 'transport' + '-ability'), where 'un-' meant 'not' and 'transportability' indicated 'the capability of being transported'.

'transport' comes from Latin 'transportare' ('trans-' meaning 'across' + 'portare' meaning 'to carry'); it passed through Old French (transporter) and Middle English (transporten/transport) before yielding modern English 'transport', to which the suffix '-ability' was later added to mean 'capability of being transported', and then the negative prefix 'un-' was prefixed to form 'untransportability'.

Originally related to the action 'to carry across', the root developed a nominal sense of 'the capability or fact of being transported' with '-ability'; adding 'un-' later produced the meaning 'not capable of being transported', which is the current sense.