Conspiracy theories can most of the time be very easy to debunk. Mostly it just requires some research and the use of logic. But, some conspiracy theories can be difficult to debunk as well. This of course has nothing to do with the evidence. As I have already stated that tends to be easy to debunk.
It's the large amount of so called evidence conspiracy theorists tend to present, or the fact that the evidence presented is simply made up. Both of these reasons can actually make it difficult to debunk some conspiracy theories simply because it can be so frustrating and time consuming to prove it's false.
Conspiracy theorists will sometimes present large amounts "evidence" to try to prove what they believe in is real, it can be time consuming for many skeptics who debunk this type of stuff because unlike many conspiracy theorists, they will take the time to do the research to find out if any of this is true or not, rather then rely on someone's accusations that has been seen as solid proof of a conspiracy. An example of this would be the alleged cover up of knowledge of extra-terrestrial technology and contact.
There is a lot of alleged evidence out there that the United States government has
extra-terrestrial technology, and has even made contact with aliens. Now while this
stuff has mostly been refuted and/or dis-proven, there is a lot of it,
and I mean a lot of it, and new "evidence" seems to pop up every year,
so debunking this stuff (or any number of conspiracy theories) can
become a full time job for some skeptics. This type of thing can wear down a skeptic and cause them to retire from debunking, even the really good ones.
What makes it harder is that often these pieces of "evidence" that conspiracy theorists presents is completely made up, so sometimes a skeptic will look for something to either refute or confirm that piece of evidence when there is nothing to refute or confirm, and it just becomes a wasteful wild goose chase. An example of this would be FEMA prison camps.
Besides the fact that these locations of where these camps allegedly are usually just nothing more then misidentified buildings and military bases, for a lot of these alleged locations nothing exists at all. In fact when I was doing some co-research into one of them with Autistic Skeptic, I investigated the location of one in Oregon that claimed to be an old Japanese interment camp that was refurbished, and as it turned out, the old interment camp never even existed in the first place, so I was basically wasting my time before I finally found out that this place didn't even exist. Not to mention that fact that I was very frustrated as well trying to find this alleged place.
Another thing conspiracy theorists will sometimes do is that they will add on to already refuted and discredited evidence. A great example of this would be the belief that the World Trade Center towers were brought down in a controlled demolition.
Many conspiracy theorists believe that the towers were brought down by explosives that were planted inside the building. When a skeptic points out that no one ever saw these explosives planted inside the buildings, the conspiracy theorists will claim that it was thermite paint. When a skeptic points out that thermite has never been detected in any independent tests, a conspiracy theorist will claim it was nano-thermite. When a skeptic points out that there is no such thing as nano-thermite, a conspiracy theorist will usually say that is what the government wants you to believe (assuming they haven't declared the skeptic a dis-information agent at some point in the conversation) and will continue to use old, refuted evidence.
At that point most skeptics would declare the conversation a PRATT (point refuted a thousand times) because they know it would be pointless to continue this cycle of refuting claims when the refuting is going to continue to be ignored and they just stop arguing with them. In fact this happens a lot with many conspiracy theorists' claims, and it can be very frustrating and angering for some skeptics (although some, especially those who were once conspiracy theorists themselves, will take pity on them).
So in the end it becomes a battle between people who will do the research and between people who will simply believe whatever they are told when it fits their world view.