Understanding Nyquist rate
1) The sampling rate has to be above twice the bandwidth, or twice the highest frequency.  The shorter the time you sample, the higher the sampling rate has to be ABOVE 2x highest frequency.

2) The signal has to be strictly bandlimited to at (or within) some frequency range below 0.5 sampling rate for no loss in information during reconstruction to occur.  Note that any sharp corners or steep edges in your signal imply an extremely high bandwidth.  

Note also that any time-limited signal (e.g. not infinite in duration) has infinite bandwidth, thus will not be strictly bandlimited, so there might always be some error in reconstruction from samples.  This error can be reduced to the noise floor by sampling longer at a higher sample rate, which is why (in the real world) one should always use some reasonable margin above the theoretical Nyquist rate (which might be OK for imaginary, perfect, and infinite signals, as written on some chalkboard).