There's a general answer to your question. But based on something specific you said, there's another answer based on a misunderstanding.

Specific issue: Mounting the lens too close to the image plane

The lens has a focal length of 39 mm. Let's rearrange the thin lens formula, and see what happens when the image plane distance \$d_\text{i}\$ (i.e., how close the lens is mounted to the sensor) is less than the focal length. The object plane distance \$d_\text{o}\$ is the distance to the object being photographed:

$$ \begin{align} {1\over f} &= {1\over d_\text{o}} + {1\over d_\text{i}} \\ {1\over d_\text{o}} &= {1\over f} - {1\over d_\text{i}} \\ d_\text{o} &= \frac{f d_\text{i}}{d_\text{i} - f} \end{align} $$

Notice that if \$d_\text{i} < f\$, the denominator is negative, meaning that the lens cannot focus on anything in front of it; the plane of object focus is behind the lens, within the lens's focal length.

Said another way: for converging lenses, the region between the lens's rear and front 'focal planes' (roughly, within 1 focal length in front of or behind the lens) cannot be focused on or imaged.

In fact, mathematically speaking, using the thin lens formula, the focal length is defined as the image distance \$d_\text{i}\$ when the object is at infinity:

$$ \begin{align} {1\over f} &= {1\over d_\text{i}} + {1\over\infty} = {1\over d_\text{i}} \\ \therefore f &= d_\text{i} \end{align} $$

In your case, mounting the lens any closer than ~39 mm to the sensor won't yield a useful system at all.

General answer: Yes, image distance affects resolution

For a particular lens make/model, ignoring copy variation (put another way, assuming a particular lens is perfectly manfuactured), that lens's performance can be completely characterized by its angular resolution.

That is, given an incoming ray of light entering the lens at a given angle \$\theta\$ from the optical axis, with a small differential region \$\Delta\theta_\text{tangential}\$ by \$\Delta\theta_\text{sagittal}\$ the lens will have a certain resolution. We don't normally describe and report angular resolution though; it's easier to think about the lateral linear resolution of the lens when its angular resolution subtends a given linear distance at the image plane.

MTF (Modulation Transfer Function) charts for lenses describe the spatial resolution of the lens in "\$x\$ line pairs/mm" at a given linear distance \$d_\text{i}\$ from the center of the imaging plane. But that's really just two legs of a right triangle that could equally describe angular "line pairs/degree" at a given angular deflection from the center of the imaging plane. If the imaging plane moves further from the lens by a small factor of \$S > 1\$ (which according to the thin lens formula, equates to focusing on a closer subject), the lens's angular resolution doesn't change. Instead, the projected image plane would be larger, and the linear resolution would be reduced by the same factor S: "\$x/S\$ line pairs/mm" at a distance of \$S\times d_\text{i}\$.