Will entropy be lost by using a DRBG? Lets assume we have a DRGB (deterministic random bit generator) which is seeded by a good true RBG (random bit generator). Before any bit has been read from the DRBG, the entropy is clearly the number of bits of the seed.    

But is entropy lost, when I read out the bits of the DRBG?
From an information theoretical point , one could say that entropy will diminish by 1 with every bit I read from the DRBG.
But how could this be defined from a complexity theoretic point?
Does there exist a precise mathematical definition of a "complexity theoretic entropy measure" ?

Maybe that question sounds a bit philosophical, but it also has practical impact, because one can decide when its time to reseed.
A Deterministic Random Bit Generator (DRBG) would typically be used, when you have entropy input that is either 


biased,
inefficiently generated, or
both of the above.


If you have a True Random Bit Generator that outputs unbiased bits efficiently, there is no apparent reason to use a DRBG in the first place. This is particularly true in case you require information theoretic security. Using a DRBG means you get pseudo random bits with computational security, typically expressed in the conventional way as 128-bits of security, 256-bits of security, etc. 

This means that reseeding of DRBG, such as NIST SP 800-90A, should not be expected to be designed to address loss of entropy in the information theoretic sense, but only in a practical sense. It is done to reduce the risks (not eliminate the risks) associated with internal states being compromised through side channel attacks, etc.