During the first moon landing (Apollo 11) Neil Armstrong and Buzz Aldrin did in fact have a really difficult time getting the flag into the moon’s surface deeply enough to get it to stay upright.

The lunar surface is a mixture of very densely compacted dust and fractured rock.

Here are Buzz Alrdin’s words on the subject:

“During a pause in the experiments Neil suggested we proceed with the flag. It took both of us to set it up and it was nearly a disaster. Public Relations obviously needs practice just as everything else does. A small telescoping arm was attached to the flagpole to keep the flag extended and perpendicular. As hard as we tried, the telescope wouldn’t fully extend. Thus the flag, which should have been flat, had its own unique permanent wave. Then to our dismay the staff of the pole wouldn’t go far enough into the lunar surface to support itself in an upright position. After much struggling we finally coaxed it to remain upright, but in a most precarious position. I dreaded the possibility of the American flag collapsing into the lunar dust in front of the television camera.” (Excerpt taken from the book, “Apollo Expeditions to the Moon” published by NASA, SP-350, 1975)

Armstrong and Alrdin twisted the flag staff back and forth while pushing down on it as hard as they could to get it just a little bit embedded into the lunar surface.

Armstrong reported during the post-mission press conference, “We had some difficulty, at first, getting the pole of the flag to remain in the surface. In penetrating the surface, we found that most objects would go down about 5, maybe 6, inches and then it would meet with a gradual resistance. At the same time, there was not much of a support force on either side, so we had to lean the flag back slightly in order for it to maintain this position.” (http://www.hq.nasa.gov/office/pao/History/alsj/a11/a11.step.html)

It has been reported, but not verified, that Aldrin said he observed the Apollo 11 flag fall down from the blast of the ascent stage engine when he and Armstrong lifted off to rendezvous with Michael Collins in the orbiting Command Module.

Beginning with Apollo 12, the flag poles were strengthened so that astronauts could use the hammers they brought for collecting rock samples to pound the flag poles down far enough into the lunar surface to keep them securely in place.