This section of the piece has four phrases, each of which are four measures long, and there are no key changes.
The first phrase contains a half cadence which lasts for the whole fourth measure.
The second phrase has contrasting material and ends on what feels like a PAC but isn't truly one since the melody ends with a re mi do. It still has a stable feeling of a period with two phrases and one would expect the music to move on to new material, but Beethoven instead decides to make the third phrase essentially identical to the second. This immediately takes away any sense of stability that the second phrase had.
The stability is taken away again because the authentic cadence of the third phrase lasts only one beat (the second phrase had three beats of the tonic chord) and moves directly to the fourth phrase.
This fourth phrase is different from the other two phrases and finally arrives at a stable PAC that lasts for a whole measure before moving on to the new material.
I'm having a hard time placing this in terms of period structure. It fits the double period formula of four phrases, but since the second and third phrases are about as weak as an authentic chord can get, I would say that this whole 16 measure is one period. The second and third phrases are parallel and the other relationships between phrases are contrasting.