Type Ia supernovae are widely accepted to be the outcomes of thermonuclear explosions in white dwarf stars. However, many details of these explosions remain uncertain (e.g. the mass, ignition mechanism, and flame speed). Theory predicts that at very late times (beyond 1000 d) it might be possible to distinguish between explosion models. Few very nearby supernovae can be observed that long after the explosion. The Type Ia supernova SN 2011fe located in M101 and along a line of sight with negligible extinction, provides us with the once-in-a-lifetime chance to obtain measurements that may distinguish between theoretical models. In this work, we present the analysis of photometric data of SN 2011fe taken between 900 and 1600 days after explosion with Gemini and HST. At these extremely late epochs theory suggests that the light curve shape might be used to measure isotopic abundances which is a useful model discriminant. However, we show in this work that there are several currently not well constrained physical processes introducing large systematic uncertainties to the isotopic abundance measurement. We conclude that without further detailed knowledge of the physical processes at this late stage one cannot reliably exclude any models on the basis of this dataset.