re-eligibility
/riːˌɛlɪdʒɪˈbɪlɪti/ /rɪˌɛlɪdʒɪˈbɪlɪti/(also reëligibility)
noun
The state or condition of being eligible for something for a second or subsequent time; especially suitability for re-election to a particular office.
Origin
Late 18th century. From re- + eligibility, after re-eligible.