The goal is to switch from "getting ideas" (which is sort of level 1 entrepreneurism) to "seeing problems" (which is, in my estimation level 2). This is important because 'brilliant idea' but can't answer the question 'what problem does it solve?' is not worth spending a lot of time on, from a money making perspective (can be from a fun perspective but that is another comment).
So hopefully you're keeping a diary/journal/notebook of these "every other day" ideas, and once you've got a couple dozen, maybe a hundred, you can start asking questions based on the ideas you come up with. Things like "What do I spend my time thinking about?", "What problem spaces are my ideas clustered around?", "Given that they have been done by other people, what was it that made them obvious in retropsect?", and my personal favorite, "Where is the hole in these ideas?"
If you have the ability to generate ideas, you can leverage that into the ability to see where changes will be needed or could be presented. Sometimes existing ideas have "baked in" assumptions (like people assuming you'll have a car so you need a gas mileage app) sometimes they are more subtle. If the underlying assumptions have changed (like it costs too much to make gas out of algae because oil is less than $75 a barrel) ideas that used to not make sense might start making sense, and then you look at changes that are going on around you whether it is spending habits, climate change, or population demographics, and try to ask questions about ideas those changes will make useful in the future.
On an unrelated topic, trying to cultivate an appreciation for "learning stuff" will serve you well, as it can be the only reward you get for the time invested. Appreciating the value of knowing, and knowing well the 'new stuff', will help with the motivation. If you think "10 ideas, all worthless because they are already done." that is demotivating, but "10 ideas, learned 10 new things, score!" you'll be much happier with the outcome. And while you may not realize it now, if you actually do learn the stuff that the idea entailed then you will start to recognize in your own thinking ideas that are probably already out there and more rapidly converge on solutions to problems that are unlikely to have been implemented yet.
Outside of software, it's obvious that "it already exists" doesn't stop anyone. Does the long list of Italian restaurants, gastropubs or microbreweries stop anyone from starting another one, with their unique twist?
Even in software, did existing social networks stop Facebook from starting another one and taking over the top spot?
Does the existence of "a web application framework" stop anyone from building a better one that matches their opinions/approach?
The only real sin would be to make an exact copy of something that already exists without making your version better in some way. Make it more user-friendly, more powerful, more configurable, cheaper, more business-friendly, etc.
You don't HAVE to trash it, you choose to. :)
Is being first to an idea the important part? It seems that not being first demotivates you because your passion is invested in being new and unique not in what you are actually building. When the uniqueness has gone, you lose interest.
You're in love with the idea of having a great idea.
Next time you get an idea you have two options :-
* Research FIRST, then be glad if it already exists, it's proof your idea is a good one and you're free to move & spend your time on something else.
* If your heart is set on working on something see the others as competition, learn from their examples, what do they charge, where they advertise, who writes about them. Learn what they're bad at and improve up on it. For the customers you serve you'll always be the first!
Even an incremental innovation will separate you from the pack.
You must always see niche markets as opportunity markets where you can fill.
Big companies are great to have around when you are trying to fill a niche market. Grow big enough and they'll buy you out.
Apart from the concept of addressing a niche market, I think you should try keeping this in mind:
"being everything to everyone" is the worst way to start an idea of.
Remember, FB started out as a social network for students, now it's everyones social network, which would explain why smaller niche networks have grown reasonably big (Pinterest, Instagram, etc.).
Doing something better is the idea that no one can take away from you.
But instead, try to make things you need. If someone else has already made them it saves time, you can use it.