There is almost no history of this for the Dáil - nine TDs resigned in sympathy with the so-called "army mutiny" in 1924, but none of them fought the seven subsequent by-elections. Kevin Boland also resigned from the Dáil in 1970 in the wake of the arms crisis, but did not fight the subsequent by-election either (he did have a go in the next general election but lost). Purist Republican theorists of course insist that the entire 1918 election in Ireland should be retrospectively given the status of a plebiscite, but nobody seems to have argued this at the time.
I have to say that it doesn't impress me all that much as a political move. Referendums, as we are seeing in Ireland at the moment, are referendums, and elections are elections; and if Parliament takes a decision that people disagree with, a by-election result in one seat won't change that (and historically did not do so in 1986 or in 1912). The fact that I happen to agree with Davis on the substance (as I would have done in 1912, but did not in 1986) doesn't change the fact that this is essentially a stunt which will do nothing to change the legislation (which may yet be blocked in the House of Lords or in the courts); the only winner will be Davis personally. Sure, he'll get some nice publicity for embarrassing the government; but I would much rather have the focus on their coalition with the DUP.