A revolutionary feature of emerging media services over the Internet is their ability to account for human perception during service delivery processes, which surely increases their popularity and incomes. In such a situation, it is necessary to understand the users' perception, what should obviously be done using standardized subjective experiences. However, it is also important to develop artificial quality assessors that enable to automatically quantify the perceived quality. This efficiently helps performing optimal network and service management at the core and edges of the delivery systems. In our article, we explore the behavior rating of new emerging artificial speech quality assessors of VoIP calls subject to moderately bursty packet loss processes. The examined Speech Quality Assessment (SQA) algorithms are able to estimate speech quality of live VoIP calls at run-time using control information extracted from header content of received packets. They are especially designed to be sensitive to packet loss burstiness. The performance evaluation study is performed using a dedicated set-up software-based SQA framework. It offers a specialized packet killer and includes the implementation of four SQA algorithms. A speech quality database, which covers a wide range of bursty packet loss conditions, has been created and then thoroughly analyzed. Our main findings are the following: (1) all examined automatic bursty-loss aware speech quality assessors achieve a satisfactory correlation under upper (> 20%) and lower (< 10%) ranges of packet loss processes; (2) they exhibit a clear weakness to assess speech quality under a moderated packet loss process; (3) the accuracy of sequence-by-sequence basis of examined SQA algorithms should be addressed in detail for further precision.