Actually, Missouri did secede. The legislature assembled a quorum in Springfield and the governor signed it.
More accurately, Missouri had two state governments during the war between the states.
when the war began, Governor Jackson’s administration was in power in Springfield in 1861.
Jackson and his followers retreated upon threat from Union troops, and moved or set up government in Neosho.
Gamble was elected provisional governor in Springfield by Union sympathizers and others who remained, setting up a military governorship.
Jackson’s faction passed a bill favoring secession, but the quorum was never verified, and one account disputes it, casting some doubt on the procedure.
Jackson died in office in the provisional government in 1862, and Reynolds succeeded him. The provisional government was driven out of Missouri altogether into Marshall, Texas for the remainder of the war between the states.
Gamble died in office in the Union government in 1864, and Hall succeeded him.
Hall died in office in the Union government in 1865, and Fletcher succeeded him.
Very possibly, the presence of the Union Army under John C. Fremont kept Missouri in the Union during the war.