Do governments always grow until they drain the country?
Almost always yes.
Does wealth distribution ratios take down a country?
Very unlikely. I see little correlation to when a country falls and its wealth distribution. The ratio may change with modern technology, but the majority of peasant revolts have been squashed. The vast majority of governments have been the rule of the very few and powerful over the rest.
Actually, I would say that it's wealth distribution ratios that, indeed, do take down a country.
Yes, there is the example that is Rome.
But there's also the example of the USSR. The maldistribution of wealth there was pouring too much into its military and for its political leaders.
The same thing happened to Czarist Russia prior to the formation of the USSR. Again, the maldistribution of wealth was focused into fighting World War I and into the aristocracy and other elites.
The Chinese Communist Party was formed out of the May 4th Movement. The May 4th Movement was a reaction to the Treaty of Versailles ending World War I. What happened was China had sent a labor force to help the Allies to free up British and French troops so they could be used for fighting instead. The understanding was that China would do this and, in exchange, they receive the province of Shandong. Shandong was controlled by Germany before the war, captured by Japan afterwards, and China wanted it back. But the treaty totally ignored the will of China and ceded the province to Japanese control. With previous exploitation of China by Western powers building up pressure, this was too much for the Chinese people and forced them to resist the West. The maldistribution here was the exploitation of the Chinese people to foreign banks who loaned them money for infrastructure projects and the like borrowed by an ineffectual administration that could only pay off the minimum and kept China in debt to them.
The French Revolution occurred because of maldistribution of wealth. The French king had bankrupted the country by borrowing funds to give to the colonies during the American Revolution. This increased the debt the French king had accrued to pay for earlier wars with Britain. This, along with consecutive poor grain harvests, incensed the French people to revolt against the royalty and aristocracy and institute a republic.
Now, granted, governments fall for very many reasons. But I think that a growing wealth gap is an indicator of a vulnerable government.