I don't have enough reputation to comment, so I'll try an answer instead.
If Eclipse is intermittently compiling / running in the background, it might be that it tries to compile the Android source codes for method(s) you're referencing in your Android project(s). One way to get around this is to create a zip-format file of the Android source codes directories, for example, zip the android-sdk\sources\android-19
directory into a single zip file and point Eclipse to this zip file.
Repeat this step for other android source codes directories that you have downloaded via the Android SDK Manager, so you might end up with something like android-19.zip, android-18.zip, android-17.zip, etc.
Use 7-zip to zip the directories. It's a free software (it's released under GNU LGPL licence).