The problems that have occurred are the most disparate, the first thing to do is to update your server or ask the ISP to do it especially the cURL must be updated. This will solve many problems with PayPal, Ebay modules and also with many modules that connect to social networks such as FB even on platforms other than PrestaShop.
PayPal response:
SILOVER -> name = LIVE6.API.1 & silo_version = 880 & app = appdispatcher_apit & TIME = 2810113364; domain
TIMESTAMP -> 2015-02-25T07: 49: 59Z
It has been a few days that both the prestashop development team and paypal have been working to solve the problems. To understand what happened, we need to take a step back, at the end of 2014 a serious security flaw in the SSL protocol was discovered and we rushed to remedy it. On February 22, 2014, communication through the fsockopen protocol of the PayPal module for PrestaShop mysteriously stops working and this causes many users inconvenience and the inability to use it. Not at all, because the module usually uses cURL and only if this is not enabled does it fall back on fockopen . At the same time, since January many WEB Servers have a problem with updates linked to the aforementioned security problem and the changes it has brought about, these problems are not evident therefore many do not pay attention to them especially because they had already intervened shortly before to update the systems and avoid problems. cURL consequently malfunctions, and eventually stops working.
Here for the solution : https://www.prestashop.com/forums/topic/419670-paypal-module-suddenly-stopped-working/#entry1982223