Yes they do flop when Caleb's tired, looks so funny. He looks hung over, they flop to the side, but only when he's exhausted.
Pip's ears were up when she was about 12 weeks for a few weeks, but went down again, shaving made no difference. She has a cotton coat and ears like a donkey, so if they flop, it won't effect her beauty lol.
Caleb looks are more standard. We love them both just the way they are...even if her coat mats as you look at her (we keep it short) Now her ears go up for hours, but mostly are down. The last two days, one has been up and one down. As she sleeps at the moment, both are down. If she had was standard, had a long beautiful coat, then maybe I'd tape her ears. As it is, her ears match her body and personality.
If you want the ears up, perhaps try giving some cottage cheese, it helps with cartilage. Some say leave the ears alone and some say massage them...who knows what's correct, but I guess be gentle. Tape if it matters to you. I've read that some dogs ears go up, up to a year old, most by 7 mths. Pip's 6 mths, so we still waiting to see, how she'll end up. Part of the fun of the breed