in chains of implicit rules such as for example

test.in:
    touch test.in
%.intermediate: %.in
    touch $@
%.out: %.intermediate
    touch $@

the command

make test.out

results in the following output

touch test.in
touch test.intermediate
touch test.out
rm test.intermediate

so test.intermediate is deleted since make considers it a by-product. The .SECONDARY target can be used to instruct make to keep such intermediate files. If the target is left without pre-requisites, all intermediate files will be preserved. Otherwise a list of files can be provided. As far as i know, patterns are not allowed. The resulting make file then should look like this

.SECONDARY:
test.in:
    touch test.in
%.intermediate: %.in
    touch $@
%.out: %.intermediate
    touch $@

to preserve all intermediate files. Or like this to preserve specific intermediate files:

.SECONDARY: test.intermediate
test.in:
    touch test.in
%.intermediate: %.in
    touch $@
%.out: %.intermediate
    touch $@