It looks like Retrieve on the TriggeredSendDefinition SOAP Object has picked up a bug where it doesn't retrieve any records where TriggeredSendStatus "equals" a specific value. Strangely, the "IN" operator works just fine.
AMPScript
%%[
SET @rr = CreateObject("RetrieveRequest")
SetObjectProperty(@rr, "ObjectType", "TriggeredSendDefinition")
AddObjectArrayItem(@rr,"Properties","CustomerKey")
AddObjectArrayItem(@rr,"Properties","Name")
AddObjectArrayItem(@rr,"Properties","TriggeredSendStatus")
SET @sfp = CreateObject("SimpleFilterPart")
SetObjectProperty(@sfp, "Property", "TriggeredSendStatus")
SetObjectProperty(@sfp, "SimpleOperator", "IN")
AddObjectArrayItem(@sfp, "Value", "Active")
AddObjectArrayItem(@sfp, "Value", "Active")
SetObjectProperty(@rr, "Filter", @sfp)
SET @tsd = InvokeRetrieve(@rr)
FOR @c = 1 TO RowCount(@tsd) DO
SET @row = Row(@tsd ,@c)
SET @TSDName = Field(@row ,'Name')
SET @TSDKey = Field(@row ,'CustomerKey')
]%%
Name: %%=v(@TSDName)=%%<br /> =
Key: %%=v(@TSDKey)=%%<br />
<br />%%[NEXT @c]%%
SOAP
<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<soapenv:Header>
<fueloauth>{{_token}}</fueloauth>
</soapenv:Header>
<soapenv:Body>
<RetrieveRequestMsg xmlns="http://exacttarget.com/wsdl/partnerAPI">
<RetrieveRequest>
<ObjectType>TriggeredSendDefinition</ObjectType>
<Properties>ObjectID</Properties>
<Properties>PartnerKey</Properties>
<Properties>CreatedDate</Properties>
<Properties>ModifiedDate</Properties>
<Properties>Client.ID</Properties>
<Properties>CustomerKey</Properties>
<Properties>Email.ID</Properties>
<Properties>List.ID</Properties>
<Properties>Name</Properties>
<Properties>Description</Properties>
<Properties>TriggeredSendType</Properties>
<Properties>TriggeredSendStatus</Properties>
<Properties>HeaderContentArea.ID</Properties>
<Properties>FooterContentArea.ID</Properties>
<Properties>SendClassification.ObjectID</Properties>
<Properties>SendClassification.CustomerKey</Properties>
<Properties>SenderProfile.CustomerKey</Properties>
<Properties>SenderProfile.ObjectID</Properties>
<Properties>DeliveryProfile.CustomerKey</Properties>
<Properties>DeliveryProfile.ObjectID</Properties>
<Properties>PrivateDomain.ObjectID</Properties>
<Properties>PrivateIP.ID</Properties>
<Properties>AutoAddSubscribers</Properties>
<Properties>AutoUpdateSubscribers</Properties>
<Properties>BatchInterval</Properties>
<Properties>FromName</Properties>
<Properties>FromAddress</Properties>
<Properties>BccEmail</Properties>
<Properties>EmailSubject</Properties>
<Properties>DynamicEmailSubject</Properties>
<Properties>IsMultipart</Properties>
<Properties>IsWrapped</Properties>
<Properties>TestEmailAddr</Properties>
<Properties>AllowedSlots</Properties>
<Properties>NewSlotTrigger</Properties>
<Properties>SendLimit</Properties>
<Properties>SendWindowOpen</Properties>
<Properties>SendWindowClose</Properties>
<Properties>SuppressTracking</Properties>
<Properties>Keyword</Properties>
<Properties>List.PartnerKey</Properties>
<Properties>Email.PartnerKey</Properties>
<Properties>SendClassification.PartnerKey</Properties>
<Properties>PrivateDomain.PartnerKey</Properties>
<Properties>PrivateIP.PartnerKey</Properties>
<Properties>Client.PartnerClientKey</Properties>
<Properties>IsPlatformObject</Properties>
<Properties>CategoryID</Properties>
<Filter xsi:type="SimpleFilterPart">
<Property>TriggeredSendStatus</Property>
<SimpleOperator>IN</SimpleOperator>
<Value>Active</Value>
<Value>Active</Value>
</Filter>
</RetrieveRequest>
</RetrieveRequestMsg>
</soapenv:Body>
</soapenv:Envelope>