Having lived in Spain for 2 years attempting to learn Spanish as a second language, one of the biggest challenges to language learning that I found was overcoming the embarrassment of coming across to Spanish people as "the fool" in a conversation. With all my study, and time and effort put into learning the language, I would still not comprehend the deeper meaning and function of of what people were saying. I might miss one or two words. There was always a delay in processing the information as my brain had to work twice as hard. This resulted in not being able to fully express myself in everyday interactions. It was a blow to my self confidence and I started to believe that I lacked the necessary mental capabilities to learn a second language. It is hard to go from being generally well educated and somewhat intelligent, and being socially adept in your first language to having to be like a child in another language, especially if you have fully immersed yourself in the other language´s culture and society. In the end, when I look back, it was really just a matter of applying the wrong methods to language learning. Some things were done right, but I missed out on a few key principles.
Another problem which I found was that it took a lot of courage to "dive into the deep end" of a second language. There was a tendency to hold onto my own culture and identity. It was very hard to just "let go" and hear Spanish, talk in Spanish, think in Spanish all day, every day for weeks and months on end. First of all, it is just very taxing on the brain. Second of all it feels like you are departing from your identity in a way. I think that a lot of students of second languages are obliged to learn a second language to improve their career prospects, or need the language to immigrate to new countries to improve their lives. The obligation might feel like a necessary burden that one "has to do". There isn't that natural passion and core motivation for learning the language because they love the language. Obviously there are many students who simply love languages. They might not encounter this "obligation" obstacle.
A major challenge which I think may affect a lot of students is not quite knowing where to begin. Not having a clear framework as a basic foundation to start with. It is only now, after having attempted to learn Spanish, that I have I have a better "road map" in mind, and a general framework for language learning to work with. I have met other people my age who have learnt one or two languages already, and they seemed to progress twice as fast as me with Spanish in the same period of time. This was a bit of a knock to my confidence, but looking back, I think that they knew what worked and what didn't work from past experience. They were able to apply workable concepts from day one, whereas I had to do a lot of trial and error to figure out what worked. It would have been nice to be presented with a clear framework at the start. There are just so many methods and techniques out there to language learning that it can be overwhelming.
The last thing that I will discuss is more personal to the student. A teacher won't have much control over this, and it is really just up to the student. That is: personal attitude, natural intelligence and and his/her control over their lives. All of these things kind of work together on the overall mood and motivation of the student. Sometimes there are just too many things to deal with in day-to-day life that learning of the second language falls down the list of their priorities. Less energy is available to invest towards studying and practicing the language. There is also natural intelligence. Some students just have better memories and cognitive abilities than other learners. This just means that it might take some learners longer to achieve the same results. But it won't stop you from achieving your goals. The best strategy to get around this problem is to find the best methods for language learning out there. Find methods which have a lot of "bang for buck", which means "value for the amount of effort you put in".
The key is to be aware of these obstacles and realize that every language learner faces the same challenges. You are not alone. Nothing is impossible. There is always another way to get around a problem. If something blocks your path, just go around it, and keep pushing ahead. If you work at it for long enough you'll find effective methods which work, and then it's just a matter of applying them.