Skeptics raise questions regarding verses that seem to imply God gets tired. Let's first note the Hebrew words: 'fainteth' is ya'aph, while 'weary' is yaga.

Regarding Exodus 31:17 ("and on the seventh day he rested, and was refreshed"): A need for rest? No—'rested' simply means 'desisted from exertion', i.e., stopped what one was doing. The Hebrew word for 'rest' (shabath) is used in the context of something ceasing or lacking, or in the sense of celebration (see Lev. 2:13; 23:32). 'Refreshed' literally means 'breathed'. The word actually suggests more of a sense of satisfaction as derived from a cooling air, as is apropos for the seventh day. If tiredness was what was at issue, a better word would have been ravach, or 'breathe freely'.

Regarding Isaiah 1:14: Even by itself, it's hard to see how this would give any idea that God was physically tired, and the word bears it out: it is la'ah, meaning disgusted. (This word is also used in Jeremiah 15:6).

Regarding Isaiah 43:24 ('thou hast wearied me with thine iniquities'): This time it is yaga, but there is a poetic point being made. This is made in counter-point to Isaiah 43:23, 'nor wearied thee with incense.' Isaiah 43:24 is a rhetorical hyperbole, making the point that none of God's demands upon the people were the sort to wear them out, and God counterpointing, 'No, you have worn me out with your sins.'

This is a powerful indictment in light of the fact that God said in Isaiah 40:28 that He does not get weary.