Continuous drug delivery (CDD) is used in moderately advanced and late-stage Parkinson’s disease (PD) to control motor and non-motor fluctuations (‘OFF’ periods). Transdermal rotigotine is indicated for early fluctuations, while subcutaneous apomorphine infusion and levodopa-carbidopa intestinal gel are utilised in advanced PD. All three strategies are considered examples of continuous dopaminergic stimulation achieved through CDD. A central premise of the CDD is to achieve stable control of the parkinsonian motor and non-motor states and avoid emergence of ‘OFF’ periods. However, data suggest that despite their efficacy in reducing the number and duration of ‘OFF’ periods, these strategies still do not prevent ‘OFF’ periods in the middle to late stages of PD, thus contradicting the widely held concepts of continuous drug delivery and continuous dopaminergic stimulation. Why these emergent ‘OFF’ periods still occur is unknown. In this review, we analyse the potential reasons for their persistence. The contribution of drug- and device-related involvement, and the problems related to site-specific drug delivery are analysed. We propose that changes in dopaminergic and non-dopaminergic mechanisms in the basal ganglia might render these persistent ‘OFF’ periods unresponsive to dopaminergic therapy delivered via CDD.