Pokemon keep running away and Pokestops don't drop anything when spinning. What is going on? [duplicate]

You are probably soft banned.

Soft banning occurs when the game detects that you're moving around too quickly. This can happen if:

• You use GPS spoofing to fake your current location.
• You travel in a vehicle at an excessive speed.
• You disable your GPS, travel a significant distance, then re-enable it.
• You lose data service, travel a significant distance, then re-connect.

The following are symptoms of a soft ban:

• When you throw a Pokeball at a Pokemon, it wiggles around a bit, then flees without fail.
• When you try and spin a Pokestop, it never turns purple, and you never get any items.
• You are unable to challenge or train at any gyms.

If you are soft banned, the ban will lift itself within a few hours.

Here's a video of what a soft ban looks like:

Currently, there is speculation that the soft ban mechanism functions similarly to the "bubble effect" in Ingress, the last ARG developed by Niantic. This effect is explained here:

No matter what speed you are traveling, you can perform an action as long as you haven't performed one in the last 15 minutes. Once you perform an action, a figurative "bubble" is created. This bubble expands at the rate of 60 km/h. If you travel out of this bubble, you will not be able to successfully perform actions. So, once you slow down, you have to wait for the bubble to catch up with you before you can perform actions again. After 15 minutes, the bubble goes away, and you can perform actions again even if the bubble hadn't caught up to you yet.

(For US readers, 60 km/h is approximately 37 mph.)

It's quite possible that you were soft banned for moving too quickly. The symptoms of not being able to get items from a pokestop and pokemon fleeing are exactly what happen when you are soft banned. It should only last a few hours, and for some they're able to fix it by simply force quitting the app.

If the game detects you are changing drastically varying locations too often, you will not be able to catch pokemon, and pokemon immediately run away when you do try to catch them.

This is most likely due to GPS spoofing or another cheat of some kind.

As you level up the Pokemon you come across have a higher CP (Combat Power). This means that they'll also be harder to Catch.

You can use Razz Berries (you can get these from Pokeshops) to have a higher chance of catching the Pokemon. Once you reach level 12 you also get access to 'Great balls' which will improve your chance of catching the Pokemon as well.

On top of this there are different ways of throwing your Poke balls which increase the chance of success. The Pokemon Go wiki has some more details on Curve balls and the different Poke balls available.