Given the script

$ cat save_stdin.sh 
#!/bin/bash

# save stdin
exec 3<&0

echo " intermediate output independing from stdin:"
echo "This is a test " | grep "test" | tr '[:lower:]' '[:upper:]'

# reset stdin
exec 0<&3

echo -e "n work with original stdin:"
ssh localhost grep "piped" | tr '[:lower:]' '[:upper:]'

# close saved stdin
exec 3<&-

I get as expected

$ echo "this is piped" | ./save_stdin.sh 
 intermediate output independing from stdin:
THIS IS A TEST 

 work with original stdin:
THIS IS PIPED

But if I insert a command like ssh localhost ps | wc -l before the reset, it seems to destroy the saved stdin:

#!/bin/bash

# save stdin
exec 3<&0

echo " intermediate output independing from stdin:"
echo "This is a test " | grep "test" | tr '[:lower:]' '[:upper:]'

##
ssh localhost ps | wc -l
##

# reset stdin
exec 0<&3

echo -e "n work with original stdin:"
ssh localhost grep "piped" | tr '[:lower:]' '[:upper:]'

# close saved stdin
exec 3<&-

gives

$ echo "this is piped" | ./save_stdin.sh 
 intermediate output independing from stdin:
THIS IS A TEST 
86

 work with original stdin:

How can I circumvent this (bug!?) without creating temporary files?