Hi,
Yesterday, my Droplet's MySQL was crashing all the time. I searched in the community and I saw that I had to do a swap of 512MB.
Now, the MySQL don't crash, but, when I enter to the domain, it don't sends any data and I must do a Power Cycle (but it stops again in a few minutes).
I can't access by no way until I do the Power Cycle (even Putty don't works).
How can I know what it's happening?
You should check your error logs.
MySQL Error Log: sudo cat /var/log/mysql/error.log
Apache Error Log: sudo cat /var/log/apache2/error.log
Nginx Error Log: sudo cat /var/log/nginx/error.log
Now that you have swap space, instead of processes being terminated, you are seeing everything slow down due to huge amounts of memory swapping. Try a 1GB droplet with 1 GB swap.
I would not have guessed that you would need 1GB for that, but unless you have added or modified things related to your MySQL installation, the problems you describe are indicative of low memory. When processes run out of memory, they terminate, as you were seeing in your initial question. When you added the swap space, processes weren't terminating (that we know of), but the system became unresponsive, which will happen when there is a lot of memory swapping going on.
I cannot definitively say that 1GB will solve your problem. It is just the most likely solution to the problem that you probably have, and trying that would answer the question fairly quickly. Take a snapshot of your current droplet and create a 1GB droplet using that snapshot. You don't have to destroy your current droplet. Hit the new one a few times and see if it remains responsive. If it does, you probably have your solution. If not, it didn't cost you a lot of money or time to get the answer.
If you don't want to take that step quite yet, I would recommend opening a terminal session immediately after you reboot your current droplet and run top to watch the memory use. If you see that your memory is nearly full and the swap space is filling rapidly (and possibly one of the most active processes has the word "swap" in its name), then you know that 512MB plus swap isn't enough to do what you are doing.