For example this line fails:
$ nohup for i in mydir/*.fasta; do ./myscript.sh "$i"; done > output.txt&
-bash: syntax error near unexpected token `do
What's the right way to do it?
Because 'nohup' expects a single-word command and its arguments - not a shell loop construct. You'd have to use:
nohup sh -c 'for i in mydir/*.fasta; do ./myscript.sh "$i"; done >output.txt' &