Why does repeating one word over and over again sound weird to us after some time? This effect seems to be observed with almost any word. I would say this phenomenon 'works' for longer and complex words better.

When we repeat a word over and over again, it starts to sound very weird and become only a bunch of repeating sounds. You don't even need to repeat it quickly.

Why does a word repeated many times lose its meaning and the brain can't recognize it properly any more?
This is called semantic saturation, or semantic satiation; studies of event-related potentials (brain waves) suggest that it is negatively correlated with N400 amplitude (the subjective experience of satiation increases as the N400 amplitude decreases) without any change to upstream sensory components.  As N400 amplitude indexes initial lexical integration--that is, understanding the word at hand in relation to the words that preceded it--this sugggests that semantic satiation is in fact due to some kind of habituation in the semantic processes, and not in upstream sensory processing.

Citations: 
Wikipedia on Semantic saturation

Kounios, J., Kotz, S. A., &amp; Holcomb, P. J. (2000). On the locus of the semantic satiation effect: Evidence from event-related brain potentials. Memory &amp; cognition, 28(8), 1366-1377.