hi Matt,
sorry...misunderstood...there's been too many subreport issues lately 
you're dealing with orphaned or widowed group footers correct? if this is the case, then this is not a unique problem to having subreports.
this can either be simple to deal with or quite difficult as there's lots of different scenarios that have to be accounted for when trying to fix the following...
a) the group header can become orphaned at the bottom of a page
and
b) the group footer can be orphaned at the top of a page
easiest fix is to go to the Group Expert and check Keep Group Together. however you may have groups that span more than one page so that forces a new page before.
if you don't want to use Keep Group Together than please see the attached. extract the contents and change the .txt extension to .rpt. have a look at the Design mode first as there's an explanation for the different sections used and then have a look at all of the Suppress formulas for each section. as you can see this is quite a lot of work / annoying. in Ideas Place eliminating orphaned group footers and headers has most likely been suggested a number of times.
there are sometimes easier solutions than the attached report but those are occasions when a group always spans more than one page. in this case you can
1) suppress the group footer
2) create a Details B section
3) copy the items from the group footer to details b...if you have group summaries you have to put them in a new formula and put the formula on details b
4) condtionally suppress details b so that it only appears when
{your field that your grouping on} = next ({your field that your grouping on})
5) condtionally suppress details A so that it only appears when
not({your field that your grouping on} = next ({your field that your grouping on}))
however, this method is not always ideal.
-jamie