Losing Viserion not once, but twice, marks a major blow to Dany's military forces, not to mention all the prestige that goes along with being the mother of dragons. Only Drogon and Rhaegal are left now, but is it possible there are more dragons in Game of Thrones? Daenerys always says she intends to break the wheel, and how better to do that then with a little extra dragon power?
Before Dany's dragons were born, dragons had been considered extinct for 300 years. Therefore, if there were another one somewhere out in the Known World, it's highly unlikely that it could have been kept a secret this long. That being said, Dany herself did keep Rhaegal and Viserion chained in the pyramid of Mereen for nearly two years. Both dragons were miserable and sickly during that time, and it possibly stunted their growth, making them significantly smaller than free-roaming Drogon. If someone in the Known World was hiding a dragon in secret, that animal would likely not be in the best of health, nor anywhere near as big as Daenerys's children.
So while there probably aren't any living dragons in existence at the moment, that doesn't mean there couldn't be one or two more before all is said and done.
Dany received her three dragon eggs from Illyrio Mopatis, her host and benefactor in Pentos, who helped arrange her marriage to Khal Drogo. When Illyrio gave Dany the eggs, he told her that they came from the Shadowlands beyond Asshai.
There is some debate over where exactly the first dragons originated from, but in George R.R. Martin's anthology book A World of Ice and Fire, the chapter "The Rise of Valyria" suggests a few possibilities — and Asshai is one of them. It reads:
"In such fragments of Barth's Unnatural History as remain, the septon appears to have considered various legends examining the origins of dragons... The Valyrians themselves claimed that dragons sprang forth as the children of the Fourteen Flames... In Asshai, the tales are many and confused, but certain texts — all impossibly ancient — claim that dragons first came from the Shadow, a place where all of our learning fails us. These Asshai'i histories say that a people so ancient they had no name first tamed dragons in the Shadow and brought them to Valyria, teaching the Valyrians their arts before departing from the annals."
If this second story is true, as Illyrio's gift suggests it could be, then it's possible there are more dragon eggs hidden in the mysterious Shadowlands. Now that there are not one but two Targaryen dragonriders flying around, it seems the odds are higher than ever of being able to hatch new baby dragons.
Then again, maybe it won't be necessary to go all the way to Asshai to hunt for forgotten dragon eggs. Although Drogon and Rhaegal might be named after male characters, there's no evidence that they're actually male themselves. In fact, before his death in A Feast for Crows, Maester Aemon described dragons as gender fluid. "Dragons are neither male nor female," Aemon tells Gilly. "Barth saw the truth of that, but now one and now the other, as changeable as flame."
If this is true, then there's no reason why Drogon or Rhaegal couldn't start laying eggs of their own. After all the death and loss this show inflicts on its characters, the promise of future dragon babies might be just the right, hopeful chord to strike before the end credits roll.