A site that I'm managing threw two of the following PayPal CURL errors on April 13th, within 2 minutes. Site details:
- Recently upgraded to v1.5.4 (from 1.3.5)
- PHP 5.3.29
- MySQL 5.5.42-cli
- Server OS: Linux 2.6.32-431.5.1.el6.x86_64
- Site has a dedicated SSL certificate (COMODO)

Code:
2015-04-13 05:12:37
-------------------
(live transaction) --> https://api-3t.paypal.com/nvp
Request Headers:
Array
(
[0] => Content-Type: text/namevalue
[1] => X-VPS-Timeout: 90
[2] => X-VPS-VIT-Client-Type: PHP/cURL
[3] => X-VPS-VIT-Integration-Product: PHP::Zen Cart(R) - PayPal/NVP
[4] => X-VPS-VIT-Integration-Version: 1.5.4
)


Request Parameters: {GetTransactionDetails}
Array
(
[TRANSACTIONID] => 18308746Y7415742E
[METHOD] => GetTransactionDetails
[USER] => shop_api1.xxxxx
[PWD] => ****************
[VERSION] => 61.0
[SIGNATURE] => ****************************************************xYTo
)


Response:
Array
(
[] =>
[CURL_ERRORS] => (51) SSL peer certificate or SSH remote key was not OK
)

(51) SSL peer certificate or SSH remote key was not OK
Array
(
[url] => https://api-3t.paypal.com/nvp
[content_type] =>
[http_code] => 0
[header_size] => 0
[request_size] => 0
[filetime] => -1
[ssl_verify_result] => 1
[redirect_count] => 0
[total_time] => 5.488148
[namelookup_time] => 5.487966
[connect_time] => 5.488167
[pretransfer_time] => 0
[size_upload] => 0
[size_download] => 0
[speed_download] => 0
[speed_upload] => 0
[download_content_length] => -1
[upload_content_length] => -1
[starttransfer_time] => 0
[redirect_time] => 0
[certinfo] => Array
(
)

[redirect_url] =>
)


GetTransactionDetails, Elapsed: 5516ms -- Failed
(51) SSL peer certificate or SSH remote key was not OK
Array
(
[url] => https://api-3t.paypal.com/nvp
[content_type] =>
[http_code] => 0
[header_size] => 0
[request_size] => 0
[filetime] => -1
[ssl_verify_result] => 1
[redirect_count] => 0
[total_time] => 5.488148
[namelookup_time] => 5.487966
[connect_time] => 5.488167
[pretransfer_time] => 0
[size_upload] => 0
[size_download] => 0
[speed_download] => 0
[speed_upload] => 0
[download_content_length] => -1
[upload_content_length] => -1
[starttransfer_time] => 0
[redirect_time] => 0
[certinfo] => Array
(
)

[redirect_url] =>
CURL configuration:
Code:
cURL support 	enabled
cURL Information 	7.38.0
Age 	3
Features
AsynchDNS 	No
Debug 	No
GSS-Negotiate 	No
IDN 	Yes
IPv6 	Yes
Largefile 	Yes
NTLM 	Yes
SPNEGO 	No
SSL 	Yes
SSPI 	No
krb4 	No
libz 	Yes
CharConv 	No
Protocols 	dict, file, ftp, ftps, gopher, http, https, imap, imaps, pop3, pop3s, rtsp, smtp, smtps, telnet, tftp
Host 	x86_64-unknown-linux-gnu
SSL Version 	OpenSSL/1.0.1e
ZLib Version 	1.2.3
Ideas welcomed.