I confirm it with

Version: 6.4.0.0.alpha0+ (x64)
Build ID: ae823e4633a76d13cebc6432b9e44b9b2862326b
CPU threads: 4; OS: Windows 10.0; UI render: GL; VCL: win; 
TinderBox: Win-x86_64@42, Branch:master, Time: 2019-06-26_23:06:07
Locale: de-DE (de_DE); UI-Language: en-US
Calc: threaded

Reproduced in

Version: 5.2.0.0.alpha1+
Build ID: 5b168b3fa568e48e795234dc5fa454bf24c9805e
CPU Threads: 4; OS Version: Linux 4.15; UI Render: default; 
Locale: ca-ES (ca_ES.UTF-8

and

Version 4.1.0.0.alpha0+ (Build ID: efca6f15609322f62a35619619a6d5fe5c9bd5a)

Here is a set of the same test cases (style, page setup, etc) with only one difference at the end of the FODT XML file (which was modified directly in XML-text editor). In spite of the structure of the documents is the same (it always finished on first page with P1 style and second page starts with P1 style) the second page could have header (correct) or not (wrong).

See attached extended_test_cases.zip

case_1_big.fodt
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift"/>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem ipsum dolor sit amet ....</text:p>
  </office:text>
- header on second page = yes (CORRECT)
  
case_2_several_small.fodt
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift"/>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem</text:p>
   <text:p text:style-name="P1">Lorem</text:p>
   <text:p text:style-name="P1">Lorem</text:p>
   ...
   <text:p text:style-name="P1">Lorem</text:p>
  </office:text>
- header on second page = yes (CORRECT)

case_3_big_plus_empty.fodt
- the same as case_1_big.fodt but with one additional empty P1 paragraph at the end.
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift"/>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem ipsum dolor sit amet ....</text:p>
   <text:p text:style-name="P1"/>
  </office:text>
- header on second page = no (WRONG)

case_3b_big_plus_empty.fodt
- The same as case_3_big_plus_empty.fodt but with text in last paragraph in prev section
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift">Weisse_5f_Schrift</text:p>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem ipsum dolor sit amet ....</text:p>
   <text:p text:style-name="P1"/>
  </office:text>
- header on second page = yes (CORRECT)

case_4_big_plus_small.fodt
- the same as case_1_big.fodt but with one additional non empty P1 paragraph at the end.
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift"/>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem ipsum dolor sit amet ....</text:p>
   <text:p text:style-name="P1">Lorem</text:p>
  </office:text>
- header on second page = no (WRONG)

case_4b_big_plus_small.fodt
- The same as case_4_big_plus_small.fodt but with text in last paragraph in prev section
- document ends with:
     <text:p text:style-name="Weisse_5f_Schrift"/>
     <text:p text:style-name="Weisse_5f_Schrift">Weisse_5f_Schrift</text:p>
    </text:section>
   </text:section>
   <text:p text:style-name="P1">Lorem ipsum dolor sit amet ....</text:p>
   <text:p text:style-name="P1">Lorem</text:p>
  </office:text>
- header on second page = yes (CORRECT)

Created attachment 158794 [details]
extended_test_cases.zip