Distributed automatic weather stations networks (AWSN) play an important role in modern weather forecasting and digitalization of agriculture. These networks allow to monitor various environment parameters and transmit actual data in real time to data centers, which makes possible to dramatically increase the efficiency of technical processes controlling farming. Since these networks may cover large areas, weather stations may use other stations to connect to gateways via multihop routes. The nodes are deployed outdoors and they are subject to failures due to harsh environment, deterioration of equipment, battery discharge, etc. If a station is used as a relay for other nodes, after its failure other stations may also become unavailable. To study the network reliability in this paper we propose a general methodology, consisting of six consolidated procedures, and apply the apparatus of the multidimensional alternating stochastic processes. We demonstrate the application of this analytical method for a special case of the minimal topology AWSN. General topology cases are studied with the use of the simulation approach. To study the numerical results, a discrete-event simulation model in Python language was developed. The paper presents numerical reliability analysis for three types of topologies: a simple network with three stations, a forest of ternary trees and random multihop networks with one or more gateways. In all scenarios we estimate reliability for the cases of static and dynamic routing. Different ways to enhance the distributed network reliability are discussed.