Except for short bouts of occupation by the British, from 1797-98 and 1802-13 (during which, Goa in effect became a British protectorate under Portuguese civil authority) the Portuguese faced very few threats from the outside from the late 17th century onwards. However, they had to deal with dissatisfaction from within.
The first revolt, also known as the Pinto Rebellion broke out in 1787, when several Goan priests, unhappy with the discrimination against them on the issue of promotions in the clerical heirarchy, attempted to overthrow the government. After several executions and deportations, this revolt was crushed.

The capture of Satari proved to be source of continued trouble for the Portuguese. The "Ranes" who occupied much of Satari were in a state of constant revolt for almost 150 years. It was only until 1912 that they were finally subdued.
One consequence of the British presence in Goa was the beginning of Goan emigration to Bombay, Poona, Karachi, Calcutta and various other parts of British India. Later, considerable numbers would migrate as far as British East Africa in search of better economic opportunities. The opening in 1878 of the port of Marmagoa to traffic with India, as well as the establishment of rail links in 1881 with India served to lessen Goa's isolation, but at the same time facilitated the Goan "diaspora" to British India and Africa.
In 1900, Luis Menezes Braganza founded the first Goan Portuguese-language newspaper (the "O Heraldo") which he used to criticize Portuguese colonialism in Goa. With the ascension of the Salazar regime (ie. dictatorship) in Portugal in 1926, came a supression of Goan (and Portuguese) civil liberties. In 1928, Dr. Cunha founded the Goa National Congress which was linked with the Indian National Congress which was then fighting the British to reclaim Indian independence. It must be said however, many of the christain Portuguese-speaking Goans, though disliking the Salazar regime, were inactive politically and looked with trepidation towards the possibility of merging with India.
The British left India in 1947, while the French quit their tiny possesion of Pondicherri in 1954. The Portuguese, under the dictatorial Salazar refused to leave however. In 1961, the Indian army simply moved into Goa encountering little resistance. The Portuguese thus the first European colonial power to enter India, were also the last to leave.