Vaccination is crucial in reducing child mortality and the prevalence of Vaccine-Preventable-Diseases (VPD), especially in low-and-middle-income countries like Kenya. However, non-vaccination, under-vaccination, and missed opportunities for vaccination (MOV) pose significant challenges to these efforts. This study aimed to analyze the impact of demographic and socio-economic factors on non-vaccination, under-vaccination, and MOV among children aged 0–23 months in Kenya from 2003 to 2014. A secondary data analysis of data from the Kenya Demographic Health Surveys (KDHS) conducted during this period was conducted, with a total of 11,997 participants, using a two-stage, multi-stage, and stratified sampling technique. The study examined factors such as child’s sex, residence, mother’s age, marital status, religion, birth order, maternal education, wealth quintile, province, child’s birth order, parity, number of children in the household, place of delivery, and mother’s occupation. Binary logistic regression was employed to identify the determinants of non-vaccination, under-vaccination, and MOV, and multivariable logistic regression analysis to report odds ratios (OR) and their corresponding 95% confidence intervals (CI). In 2003, the likelihood of non-vaccination decreased with higher maternal education levels: mothers who did not complete primary education (AOR = 0.55, 95% CI = 0.37–0.81), completed primary education (AOR = 0.34, 95% CI = 0.21–0.56), and had secondary education or higher (AOR = 0.26, 95% CI = 0.14–0.50) exhibited decreasing probabilities. In 2008/09, divorced/separated/widowed mothers (AOR = 0.22, 95% CI = 0.07–0.65) and those with no religion (AOR = 0.37, 95% CI = 0.17–0.81) showed lower odds of non-vaccination, while lower wealth quintiles were associated with higher odds. In 2014, non-vaccination was higher among younger mothers aged 15–19 years (AOR = 12.53, 95% CI = 1.59–98.73), in North Eastern Province (AOR = 7.15, 95% CI = 2.02–25.30), in families with more than 5 children (AOR = 4.19, 95% CI = 1.09–16.18), and in children born at home (AOR = 4.47, 95% CI = 1.32–15.17). Similar patterns were observed for under-vaccination and MOV. This information can inform strategies for bridging the gaps in immunization coverage and promoting equitable vaccination practices in Kenya.