<p>I have designed a bread mark and printed it on the Prusa i3 MK3.</p>

<p><a href="https://i.stack.imgur.com/qs5PP.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qs5PP.png" alt="Bread mark"></a></p>

<p>I wanted it to have as sharp edges as possible, so I used a triangle:</p>

<p><a href="https://i.stack.imgur.com/AMTCP.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/AMTCP.png" alt="Triangle"></a></p>

<p>However, it seems that the print cut off layers that are too thin (x-y-wise) and instead of a 1 cm high bread mark, I only have 0.5 cm.</p>

<p>What is the X-Y-resolution of the Prusa i3 MK3? In Slic3r, can I make sure that any wall is made as thick as needed for it to be printed?</p>

<p>I have the default 0.4 mm nozzle.</p>

This is dependent on the slicer and the nozzle diameter. Typically, you cannot print a wall smaller than twice the nozzle diameter because walls need an inner and outer line. Therefore, your slicer will make some cutoff and won't print walls below a certain threshold, in order to try to faithfully replicate your model.
Slic3r, I believe, will automatically go down to single line walls, but if you turn on "Detect thin walls" in Slic3r's Print Settings, more of the thin walls will be printed. Slic3r will actually reduce the plastic extruded to attempt to make even thinner walls, but there's still a limit.
With a 0.4 mm nozzle, you should design walls no smaller than 0.8 mm, or 0.4 mm at the very smallest.