How and why does downsampling reduces resolution in time
Anytime you take away "actual" data samples away by donwsampling, yes, you are loosing on finer granular data in time domain and hence reducing resolution. However, consider, the following case, an input signal is first up sampled by 2(interpolation) and then down sampled by 2, does it decrease resolution of actual data, not quite, because the upsampled new data points were anyways interpolated versions of the original data. So you have in total not lost any resolution of the actual data. So when we talk about resolution we should always be referring to resolution with reference to the actual signal data points

It's always helpful to keep in mind what happened before the down sampling. 

Almost all the time in a system, a downsampling would be happening on an "oversampled signal"(for noise reduction purposes) or preceded by upsampling for rate conversion. In both cases, the data points that would be throwing off were in any case "not required" for processing.

In summary, yes, any time you throw away actual samples of the signal you do loose on information in time domain, but as illustrated above its important to keep in mind that what is being down sampled are actual or artificial data.

Side note on Frequency Domain: Any time we down-sample a signal, we are essentially limiting the signal bandwidth that can be represented unambiguously