Mendeleev's table left holes, and most of them were filled within a generation: gallium in 1875, scandium in 1879, germanium in 1886. Element 43, sitting between molybdenum and ruthenium, refused.
It was claimed repeatedly. Names proposed for it over the decades included davyum, lucium and nipponium, and all were withdrawn or reassigned. The most substantial claim came in 1925, when Walter Noddack, Ida Tacke and Otto Berg in Berlin announced that they had found both element 75 and element 43 in platinum ores and columbite, naming them rhenium and masurium. Rhenium was real and they had it. Masurium could not be reproduced by anyone, including themselves, and the quantity of element 43 that could conceivably have been present in their samples is far below what their X-ray method could have detected. The claim is not accepted.
The reason for the difficulty was not experimental. Element 43 has no stable isotope at all, and effectively none of it exists on Earth. This is a genuine oddity, since it sits in the middle of the table surrounded by perfectly stable neighbours. The explanation lies in a rule derived by Josef Mattauch in 1934 concerning which pairs of neighbouring isobars can both be stable, and it accounts for the two gaps below bismuth, technetium and promethium, and for nothing else.
Carlo Perrier and Emilio Segre closed it in 1937. Segre had visited Berkeley and asked Ernest Lawrence for discarded parts of the cyclotron; Lawrence sent him a molybdenum deflector foil that had been bombarded with deuterons. Working in Palermo, Perrier and Segre separated from it a new radioactive substance whose chemistry matched the predictions for element 43. They named it technetium, from the Greek tekhnetos, artificial, because it was the first element made rather than found.