It is a strict rule? or approximate time?
I think its a Strict rule, Because as its automated system, and you know how it works. Automated system always pays on time.
Yeah it could be delayed if the wallet is empty.
The reason it was delayed (by a few hours only) was due to blockchain.info banning the bot's IP.
Thanks for the suggestion, any clues as to where I could start? I'll look into it.
I would start by downloading Bitcoin QT from Bitcoin.org and then you can use something like an offline version of brainwallet to create signed transactions that pays out money owed to participants. Once the bit creates the signed transaction it can push it with "sendrawtransaction". I believe that brainwallet may use blockchain.info to download the transaction history by default, however in theory you should be able to download the transaction history from your instance of QT.
Alternatively you can use something like armory to create and push transactions to the network (armory requires a full node to be running locally). It would use a seed to generate addresses and send funds to change addresses, although you can monitor the "balance" of the wallet with the xpub key which will allow you to determine all the translations associated with the seed but the xpub key would not allow you access to any of the private keys.
If a full node is too resource intensive for your VPS then you can use something like electrum which acts similar to armory, expect it uses SPV servers which is slightly less secure in regards to validating transactions you receive, however you would not be subject to those types of vulnerabilities if all you are doing is paying participants. I personally use electrum for my hot wallet and it works great for me. In theory you can program your bot to have it create transactions automatically with its console, or its GUI.