The most plausible explanation is that the blobs Fassbinder saw in 2003 that he said might be the tomb turned out to be nothing. Magnetometry and ground penetrating radar can be very difficult to interpret. You see it a lot on time team. It can tell you where to dig sometimes but just as often tells you to dig in the wrong place. Could've been a tomb they saw in the river bed or could've been a patch with a different type of sediment.
Archaeology is going on in the middle east all the time but the discoveries just aren't very sexy.
This is what wikipedia says:
Media interest was excited in 2003 by a report that the German Archaeological Institute team had discovered something that might be the tomb of the legendary king Gilgamesh. The Sumerian poem The Death of Gilgamesh describes how the River Euphrates parted after Gilgamesh died and he was buried underneath it, before the river was restored to its course. The Euphrates has changed its course since the time when Gilgamesh is supposed to have lived, and the route it followed then is now dry. In an interview, Fassbinder was careful to state that they had no solid proof and that the structure had not been excavated and they would not know unless it was, but said that magnetometric scans had revealed buried structures in the former bed of the Euphrates that matched the description in the poem. He commented that other scans of that part of the site so far were a surprisingly good match for Sumerian descriptions of Uruk as it was in Gilgamesh's day, making the theory that the poem was also right about the tomb more plausible.
The invasion of Iraq happened shortly after the announcement. The site at Uruk escaped looting during the war, and further investigations have been done there since then, but there has been no further public comment on the possible tomb. When asked about it by an independent researcher, Fassbinder was reticent, saying only that the media coverage had been exaggerated and that he had only said that it might be the tomb of Gilgamesh.