in the sample bellow, when a \part have only one \chapter inside, the footnote number does not reset properly, but if there is more than one chapter in a part, it resets fine.
\starttext
\setuphead[chapter][number=no,page=no]
\setuphead[part][placehead=yes,number=no,page=no]
\setupfootnotes[way=bychapter]
\part Part I
\chapter Chapter 1
Text Chapter 1\footnote{footnote 1 chapter 2}
\part Part II
\chapter Chapter 2
Texto chapter 2\footnote{Footnote 1 chapter 2. This footnote should be 1!!}
\chapter Chapter 3
Texto chapter 3\footnote{footnote 1 chapter 3}
\part Part III
\chapter Chapter 4
Texto chapter 4\footnote{footnote 1 chapter 4}
\part Part IV
\chapter Chapter 5
Text chapter 5\footnote{footnote 1 chapter 5. This footnote shlould be 1 too.}
\stoptext