The active K2V star $epsilon$ Eri hosts the most nearby known extrasolar planet. With an angular separation of about 1 on average, and an age of a few to several hundred Myrs, $epsilon$ Eri b is one of the prime candidates for becoming the first definitive extrasolar planet imaged directly. We present a multi-epoch deep differential imaging survey performed with NACO-SDI at the VLT with the aim of finding the planet. The results are combined with recent astrometry in an attempt to further constrain the detection limits. No convincing candidate is found among the many coherent structures that constitute the residual speckle noise, which is the dominant noise at small angular scales. We present our detection limits, compare them with the estimated brightness of $epsilon$ Eri b, and analyze how the limits can be improved further. It is found that integration time remains a very important parameter for achieving good results, even in the speckle-dominated regimes. The results yield new, improved upper 3$sigma$ limits on the absolute H-band (1.6 $mu$m) brightness of the 1.55 $M_{rm jup}$ companion of 19.1 to 19.5 mag, depending on the specific age of the system.
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