So why has the Cuban government not asked them to leave?
The simple answer to that is that they have.
The United States assumed territorial control over the southern portion of Guantánamo Bay under the 1903 Cuban–American Treaty of Relations. The United States exercises complete jurisdiction and control over this territory, while recognizing that Cuba retains ultimate sovereignty. The current government of Cuba regards the U.S. presence in Guantánamo Bay as illegal and insists the Cuban–American Treaty was obtained by threat of force and is in violation of international law. Some legal scholars judge that the lease may be voidable.
After the Cuban Revolution, Dwight D. Eisenhower insisted the status of the base remain unchanged, despite Fidel Castro's objections. Since then, the Cuban government has cashed only one of the rent checks from the U.S. government, and even then only because of "confusion" in the early days of the leftist revolution, according to Castro. The remaining un-cashed checks made out to "Treasurer General of the Republic" (a title that ceased to exist after the revolution) are kept in Castro's office stuffed into a desk drawer.
They've asked (e.g. in 2016). The United States (US) has not left. The basis of not leaving (again from Wikipedia):
In 1934 a new Cuban-American Treaty of Relations reaffirming the lease granted Cuba and its trading partners free access through the bay, modified the lease payment from $2,000 in U.S. gold coins per year to the 1934 equivalent value of $4,085 in U.S. dollars, and made the lease permanent unless both governments agreed to break it or until the U.S. abandoned the base property.
The US has never agreed to ending the treaty, and it requires both parties to agree to end it.
Reading the sources implies that ending the treaty is something that Fidel Castro requested repeatedly, but I can't find a primary source actually stating that.