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Automatic blood vessel segmentation from retinal images plays an important role in the diagnosis of many systemic and eye diseases, including retinopathy of prematurity. Current state-of-the-art research in blood vessel segmentation from retinal images is based on convolutional neural networks. The solutions proposed so far are trained and tested on images from few available retinal blood vessel segmentation datasets, which might limit their performance when given an image with retinopathy of prematurity signs. In this paper, the performance of three high-performing convolutional neural networks for retinal blood vessel segmentation is evaluated in the context of blood vessel segmentation on retinal images exhibiting retinopathy of prematurity. The main motive behind the study is to test if existing public datasets suffice to develop a high performing predictor that could assist an ophthalmologist in retinopathy of prematurity diagnosis. To do so, the authors created a dataset consisting solely of retinopathy of prematurity images. Retinal blood vessels are manually labeled in the images by two observers, including an ophthalmologist experienced in retinopathy of prematurity treatment. Experimental results show that all three solutions have difficulties in detecting the retinal blood vessels of infants due to a lower contrast compared to images from public datasets as demonstrated by significant drop in classification sensitivity. All three solutions segment alongside retinal also choroidal blood vessels which are not used to diagnose retinopathy of prematurity, but instead represent noise and are confused with retinal blood vessels. Through observations and numerical analysis of experimental data, it is concluded that existing solutions for retinal blood vessel segmentation need improvement oriented toward using more detailed datasets or deeper models in order to assist the ophthalmologist in retinopathy of prematurity diagnosis.