To the point here, the theme offers an obvious opportunity for a rising line in the minor, an opportunity that Beethoven does not exploit, however, as we shall see below. There is one rising line among the 32 variations, but it is in the maggiore variation 14.
The chromatic chaconne bass in bars 1-6 moves against a rising line in the right hand, the overall result being to move both bass and melody from ^1 to ^5, but of course in opposite directions. The wedge goes one step further in the sforzando subdominant chord but then the simple octaves fall sharply (and quietly). The potential for a variant of an ascending Urlinie, however, is introduced by that subdominant chord -- I have marked how it might be realized in scale degrees. As it stands, the clearest implicit figure is a displaced neighbor G5-Ab5-G4 (bars 6 and 7).
In the variations, Beethoven makes much of the dramatic contrast between the first six bars and the cadence. Since he includes the rise-and-fall gesture in many cases, the clear expression of a rising line is not possible. Variation 5 is typical. The arrows at (a) chart the wedge in the melody, which does reach ^6, but then the convoluted drop-off leaves one assuming an implied completion of the neighbor figure, so, G6-Ab6-(G6).
The primary impediment to an ascending Urlinie in the variations is Beethoven's abandonment of the subdominant supporting ^6 for an expanded dominant, as in Variation 6, where bars 6-7 are a dominant seventh or ninth.
Variation 12 is the first of five maggiore variations. The arrow points to the sixth scale degree that ought to make a continued ascent in the cadence easy to manage.
Variation 14, finally, does realize a rising line. An initial ascent brings ^3 (at "x") up to ^5 (at "y"). A first attempt at the line from ^5 to ^8 follows (see "z"), and bars 7-8 do the work with clarity and resolve (thus, ^5 in bar 3 moves to ^6 in bar 7 and the line then finishes the ascent).