Akhenaten 17 - 3 = 14 (Let's move things along here. Known primarily for his monotheistic enforcement of a lockdown on Egyptian polytheism, but evidence shows he cared little for foreign policy and enriched his own religious cult at the expense of the happiness of his citizens. This is not a bold, charismatic, capable leader--this is a selfish, uninterested, inept one who lost much Egyptian national power despite having followed on the economic and military prowess of prior pharaohs. But hey, at least they made interesting art during Akhenaten's reign right?)
Alexander II (Russia) 21
Alexios I Komnenos (Byzantium) 22
Atahualpa (Inca) 22
Aurangzeb (India / Mughal) 21
Calvin Coolidge (America) 16
Coloman the Learned (Hungary) 18
Edward the Confessor (England) 20
Hezekiah (Judah) 19 + 1 = 20 (This guy ought at least be 20--a monotheist who successfully defended Jerusalem against the Assyrian Empire with a combination of luck (ala Hojo Tokimune), and strategy (Siloam Tunnel, fortification of Jerusalem with walls and towers, formation of an alliance with Egypt), and made sweeping religious reforms of which his people overall approved (the Passover tradition he renewed saw celebration such as had not been seen in Jerusalem since the days of Solomon, and he also oversaw the compilation of the books of Isaiah, Proverbs, Song of Songs and Ecclesiastes according to the Talmud). Hezekiah also has a well-attested record biblically and archaeologically.)
Menawa (Creek) 21
Napoleon III (France) 22
Oliver Cromwell (England) 8
Powhatan (Powhatan Confederacy) 19
Tin Hinan (Berbers / Tuaregs) 5
Vercingetorix (Celts / Gauls) 21
Yongle Emperor (China) 21
I'm aware of this. To all appearances, Thutmoses III had no problems with his stepmother/aunt and merely defaced her public statues for political reasons, but I am of the persuasion that Akhenaten also was purged for political reasons (that will happen when you strip power away from the most powerful political class, in this case the priests of Amun). I'm also given to understand that he was quite popular in his early reign, but as his health declined and he withdrew from public in later years he also became less popular--the same happened to Elizabeth I.
I see no evidence of Akhenaten's popularity in his early reign (unless you mean the time before he stripped the temples and priests away, in the time he was known as Amenhotep IV, or in the time he shared the throne with his father under a coregency, and even there I see no evidence of his "popularity" as such).
On the contrary, Akhenaten was likely the source of widespread national trauma in Egypt, as discussed in
BBC's In Our Time podcast on Akhenaten, as Egyptian citizens had grown to rely on family gods and cherished them. So no, I don't think he was popular at any time in his reign. His health declining and withdrawal from public I doubt made him any more unpopular than he already was.
As for Elizabeth I, she became less popular in later years not due to her health declining and/or withdrawal from public life as such, but due to the following: 1) rising costs of war (Elizabeth was unfortunately not very successful in her foreign wars), 2) falling standard of living, 3) her granting favorable monopolies as a form of patronage, which caused
"price-fixing, the enrichment of courtiers at the public's expense, and widespread resentment." Elizabeth, however, regained popularity after her famous
Golden Speech, in which she acknowledged her errors, saying: "Who keeps their sovereign from the lapse of error, in which, by ignorance and not by intent they might have fallen, what thank they deserve, we know, though you may guess."
Akhenaten made no similar move to gain popularity or acknowledge his flaws at any time in his life that I have found.