Why do fatigue and sleep sometimes follow frequent recitation of "There is no might nor power except in Allah," while other times it is followed by a feeling of happiness?

The fatigue and sleepiness you experience when reciting "Lā hawla wa lā quwwata illā billāh" (There is no might or power except with Allah) might be from Satan, seeking to distract you from remembrance. Therefore, you should seek refuge in Allah (make Isti'adhah) and be patient. It is also possible that the fatigue is natural, and in that case, it is best to sleep until the drowsiness subsides, so that you do not supplicate against yourself, as mentioned in the Hadith. As for the happiness you find when increasing in remembrance, it is natural, for with the remembrance of Allah do hearts find joy and tranquility. So, praise Allah for this happiness and ask Him for more.