If you don't mind to use the same file for storing the output; then:
ssh user@host "command1; command2" > /local/1-2.txt
If it matters, then try something like this:
ssh user@host "command1 > /somepath/1.txt; command2 > /somepath/2.txt; ..."
scp user@host:/somepath/*.txt somelocalpath/
If you still want just a single connection, maybe this might work for you:
ssh user@host "command1; echo "this_is_a_separator"; command2" > /local/1-2.txt
sed -n '1,/this_is_a_separator/ {p}' /local/1-2.txt > /local/1.txt
sed -n '/this_is_a_separator/,$ {p}' /local/1-2.txt > /local/2.txt
The local file splitting can be done in several other ways, that was just one of them.