The active K2 V star ∊ Eri hosts the nearest known extrasolar planet. With an angular separation of about 1" on average, and an age of a few to several hundred megayears, ∊ Eri b is one of the prime candidates for becoming the first definitive extrasolar planet imaged directly. We present a multiepoch 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 ∊ 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 3 σ upper limits on the absolute H-band (1.6 μm) brightness of the 1.55 MJup companion of 19.1-19.5 mag, depending on the specific age of the system.Based on observations collected at the European Southern Observatory, Chile (NACO-SDI commissioning run 2003 August, ESO 273.C-5030 and 076.C-0027).