Former Labor senator Anne McEwen has lost a bid to introduce new evidence her legal team said would cast doubt on the ability of the Family First Party to replace resigned senator Bob Day with another Family First candidate.

The High Court is considering the eligibility of Mr Day to run for the Senate in July last year.

The make-up of the Senate hangs on the outcome, with the government requiring the support of eight of the nine remaining crossbenchers to pass legislation if Labor and the Greens combine to oppose them, now that two former senators are being scrutinised by the High Court.

The High Court is also reserving its judgment on the eligibility of former One Nation Senator Rod Culleton to run for the Senate.