No exit stamp under type D schengen visa?

Germany does not stamp passports of residence permit holders, and it is possible that the officer assumed you're a resident (most D visa holders are) and therefore did not stamp you.

If you're not a resident, you should've explained it to her and she should've stamped you out.

In this case, my recommendation would be to e-mail the police at Frankfurt Airport at bpold.frankfurt@polizei.bund.de, attaching a copy of your passport, visa and boarding pass, explain your situation and ask what to do.

This is quite an interesting case. Let's see question #1 first:

Is the exit stamp not necessary in this case?

My understanding is that it was necessary, and I think the Immigration made a mistake here.

Schengen Borders Code Article 11 states it clearly that:

1. The travel documents of third-country nationals shall be systematically stamped on entry and exit.

However there are exclusions (also in Article 11):

3. No entry or exit stamp shall be affixed:

...skipped a-f...

(g) to the travel documents of nationals of third countries who present a residence card provided for in Directive 2004/38/EC.

So it looks like the officer though that your D visa is the same as "a residence card provided for in Directive 2004/38/EC". It however is not, because the Directive 2004/38/EC only speaks about residence cards of Union citizen family members, and not about other long term visas (employment, study etc).

This is further supported by more text on Article 11:

The travel documents of nationals of third countries who are members of the family of nationals of third countries enjoying the right of free movement under Union law, but who do not present the residence card provided for in Directive 2004/38/EC, shall be stamped on entry and exit.

Thus it is not enough just to be a Union citizen family member to avoid the stamp - one must also present (not just possess) the residence card to Border control.

Since you didn't present the residence card (no mention of that in your post), you should have received the stamp.

Now, the question #2:

Will this cause issues for me in the future? (I now have one entry to Germany at the end of November, but no exit)

Theoretically possible, but unlikely.

As far as I'm aware, there is no single shared database (yet) registering Schengen entries/exits across the member countries - each country has their own database. Thus if you enter through another Schengen country next time and it happens after visa expiration, you theoretically might have to prove you didn't overstay your visa. While German authorities will have this information in their system, other countries will not know about that and would have no easy way to check it. Thus handing on your boarding pass and having other stamps outside Schengen area during this time frame would be helpful.

Saying so, practically you are unlikely to have issues. There's a number of Schengen countries where the immigration officers only stamp passports when they're in mood. Spain and Italy are typical, several times there my passport was not stamped on entry or exit, and couple times it wasn't even scanned (this never happened in Germany though).